×

Analysis and applications: the mathematical work of Elias Stein. (English) Zbl 1452.32001

Summary: This article discusses some of Elias M. Stein’s seminal contributions to analysis.

MSC:

32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
42-02 Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces

Biographic References:

Stein, Elias M.
Full Text: DOI

References:

[1] Aldaz, J. M., The weak type \((1,1)\) bounds for the maximal function associated to cubes grow to infinity with the dimension, Ann. of Math. (2), 173, 2, 1013-1023 (2011) · Zbl 1230.42025 · doi:10.4007/annals.2011.173.2.10
[2] Barrett, David E., Behavior of the Bergman projection on the Diederich-Forn\ae ss worm, Acta Math., 168, 1-2, 1-10 (1992) · Zbl 0779.32013 · doi:10.1007/BF02392975
[3] Barrett, David E.; Lanzani, Loredana, The spectrum of the Leray transform for convex Reinhardt domains in \(\mathbb{C}^2\), J. Funct. Anal., 257, 9, 2780-2819 (2009) · Zbl 1181.32002 · doi:10.1016/j.jfa.2009.04.011
[4] Beals, Michael; Fefferman, Charles; Grossman, Robert, Strictly pseudoconvex domains in \({\bf C}^n \), Bull. Amer. Math. Soc. (N.S.), 8, 2, 125-322 (1983) · Zbl 0546.32008 · doi:10.1090/S0273-0979-1983-15087-5
[5] Bergelson, V.; Leibman, A., A nilpotent Roth theorem, Invent. Math., 147, 2, 429-470 (2002) · Zbl 1042.37001 · doi:10.1007/s002220100179
[6] Bourgain, J., Averages in the plane over convex curves and maximal operators, J. Analyse Math., 47, 69-85 (1986) · Zbl 0626.42012 · doi:10.1007/BF02792533
[7] Bourgain, J., On high-dimensional maximal functions associated to convex bodies, Amer. J. Math., 108, 6, 1467-1476 (1986) · Zbl 0621.42015 · doi:10.2307/2374532
[8] Bourgain, J., On the \(L^p\)-bounds for maximal functions associated to convex bodies in \(\mathbf{R}^n\), Israel J. Math., 54, 3, 257-265 (1986) · Zbl 0616.42013 · doi:10.1007/BF02764955
[9] Bourgain, J., On the maximal ergodic theorem for certain subsets of the integers, Israel J. Math., 61, 1, 39-72 (1988) · Zbl 0642.28010 · doi:10.1007/BF02776301
[10] Bourgain, J., On the pointwise ergodic theorem on \(L^p\) for arithmetic sets, Israel J. Math., 61, 1, 73-84 (1988) · Zbl 0642.28011 · doi:10.1007/BF02776302
[11] Bourgain, J., A remark on the maximal function associated to an analytic vector field. Analysis at Urbana, Vol. I, Urbana, IL, 1986-1987, London Math. Soc. Lecture Note Ser. 137, 111-132 (1989), Cambridge Univ. Press, Cambridge · Zbl 0692.42006
[12] Bourgain, Jean, Pointwise ergodic theorems for arithmetic sets, Inst. Hautes \'{E}tudes Sci. Publ. Math., 69, 5-45 (1989) · Zbl 0705.28008
[13] Bourgain, Jean, Some new estimates on oscillatory integrals. Essays on Fourier analysis in honor of Elias M. Stein, Princeton, NJ, 1991, Princeton Math. Ser. 42, 83-112 (1995), Princeton Univ. Press, Princeton, NJ · Zbl 0840.42007
[14] Bourgain, Jean, On the Hardy-Littlewood maximal function for the cube, Israel J. Math., 203, 1, 275-293 (2014) · Zbl 1309.42023 · doi:10.1007/s11856-014-1059-2
[15] Bourgain, Jean; Demeter, Ciprian, The proof of the \(l^2\) decoupling conjecture, Ann. of Math. (2), 182, 1, 351-389 (2015) · Zbl 1322.42014 · doi:10.4007/annals.2015.182.1.9
[16] Bourgain, Jean; Demeter, Ciprian; Guth, Larry, Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three, Ann. of Math. (2), 184, 2, 633-682 (2016) · Zbl 1408.11083 · doi:10.4007/annals.2016.184.2.7
[17] Burkholder, D. L.; Gundy, R. F.; Silverstein, M. L., A maximal function characterization of the class \(H^p \), Trans. Amer. Math. Soc., 157, 137-153 (1971) · Zbl 0223.30048 · doi:10.2307/1995838
[18] S. Buschenhenke, S. Dendrinos, I. Ikromov, and D. M\"uller, Estimates for maximal functions associated to hypersurfaces in \(\mathbbR^3\) with height \(h<2\), Part I, arXiv:1704.06520 (2017). · Zbl 1418.42025
[19] Calder\'{o}n, A.-P., Commutators of singular integral operators, Proc. Nat. Acad. Sci. U.S.A., 53, 1092-1099 (1965) · Zbl 0151.16901 · doi:10.1073/pnas.53.5.1092
[20] Calder\'{o}n, A.-P., Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A., 74, 4, 1324-1327 (1977) · Zbl 0373.44003 · doi:10.1073/pnas.74.4.1324
[21] Calder\'{o}n, A.-P.; Zygmund, A., On higher gradients of harmonic functions, Studia Math., 24, 211-226 (1964) · Zbl 0168.37002 · doi:10.4064/sm-24-2-211-226
[22] Carbery, Anthony, An almost-orthogonality principle with applications to maximal functions associated to convex bodies, Bull. Amer. Math. Soc. (N.S.), 14, 2, 269-273 (1986) · Zbl 0588.42012 · doi:10.1090/S0273-0979-1986-15436-4
[23] Carbery, Anthony; Christ, Michael; Wright, James, Multidimensional van der Corput and sublevel set estimates, J. Amer. Math. Soc., 12, 4, 981-1015 (1999) · Zbl 0938.42008 · doi:10.1090/S0894-0347-99-00309-4
[24] Carleson, Lennart, On convergence and growth of partial sums of Fourier series, Acta Math., 116, 135-157 (1966) · Zbl 0144.06402 · doi:10.1007/BF02392815
[25] Christ, Michael, Hilbert transforms along curves. I. Nilpotent groups, Ann. of Math. (2), 122, 3, 575-596 (1985) · Zbl 0593.43011 · doi:10.2307/1971330
[26] Christ, Michael, Pointwise estimates for the relative fundamental solution of \(\overline\partial_b\), Proc. Amer. Math. Soc., 104, 3, 787-792 (1988) · Zbl 0694.35003 · doi:10.2307/2046793
[27] Christ, Michael, Regularity properties of the \(\overline\partial_b\) equation on weakly pseudoconvex CR manifolds of dimension \(3\), J. Amer. Math. Soc., 1, 3, 587-646 (1988) · Zbl 0671.35017 · doi:10.2307/1990950
[28] Christ, Mike, On the \(\overline\partial_b\) equation and Szeg\H{o} projection on CR manifolds. Harmonic analysis and partial differential equations, El Escorial, 1987, Lecture Notes in Math. 1384, 146-158 (1989), Springer, Berlin · Zbl 0701.35116 · doi:10.1007/BFb0086799
[29] Christ, Michael, A \(T(b)\) theorem with remarks on analytic capacity and the Cauchy integral, Colloq. Math., 60/61, 2, 601-628 (1990) · Zbl 0758.42009 · doi:10.4064/cm-60-61-2-601-628
[30] Christ, Michael, On the \(\overline\partial_b\) equation for three-dimensional CR manifolds. Several complex variables and complex geometry, Part 3, Santa Cruz, CA, 1989, Proc. Sympos. Pure Math. 52, 63-82 (1991), Amer. Math. Soc., Providence, RI · Zbl 0747.32009
[31] Christ, Michael, The strong maximal function on a nilpotent group, Trans. Amer. Math. Soc., 331, 1, 1-13 (1992) · Zbl 0765.43002 · doi:10.2307/2153994
[32] Coifman, R. R.; McIntosh, A.; Meyer, Y., L’int\'{e}grale de Cauchy d\'{e}finit un op\'{e}rateur born\'{e} sur \(L^2\) pour les courbes lipschitziennes, Ann. of Math. (2), 116, 2, 361-387 (1982) · Zbl 0497.42012 · doi:10.2307/2007065
[33] Coifman, Ronald R.; Meyer, Yves, Au del\`a des op\'{e}rateurs pseudo-diff\'{e}rentiels, Ast\'{e}risque 57, i+185 pp. (1978), Soci\'{e}t\'{e} Math\'{e}matique de France, Paris · Zbl 0483.35082
[34] Collins, Tristan C.; Greenleaf, Allan; Pramanik, Malabika, A multi-dimensional resolution of singularities with applications to analysis, Amer. J. Math., 135, 5, 1179-1252 (2013) · Zbl 1281.32026 · doi:10.1353/ajm.2013.0042
[35] Cotlar, Mischa, A unified theory of Hilbert transforms and ergodic theorems, Rev. Mat. Cuyana, 1, 105-167 (1956) (1955) · Zbl 0071.33402
[36] Cowling, Michael, The Kunze-Stein phenomenon, Ann. Math. (2), 107, 2, 209-234 (1978) · Zbl 0363.22007 · doi:10.2307/1971142
[37] David, Guy, Op\'{e}rateurs int\'{e}graux singuliers sur certaines courbes du plan complexe, Ann. Sci. \'{E}cole Norm. Sup. (4), 17, 1, 157-189 (1984) · Zbl 0537.42016
[38] L. Deleaval, O. Gu\'edon, and B. Maurey, Dimension free bounds for the Hardy-Littlewood maximal operator associated to convex sets, arXiv:1602.02015 (2016). · Zbl 1395.42044
[39] Ehrenpreis, L.; Mautner, F. I., Uniformly bounded representations of groups, Proc. Nat. Acad. Sci. U.S.A., 41, 231-233 (1955) · Zbl 0064.02604 · doi:10.1073/pnas.41.4.231
[40] Fefferman, Charles, Inequalities for strongly singular convolution operators, Acta Math., 124, 9-36 (1970) · Zbl 0188.42601 · doi:10.1007/BF02394567
[41] Fefferman, Charles, The multiplier problem for the ball, Ann. of Math. (2), 94, 330-336 (1971) · Zbl 0234.42009 · doi:10.2307/1970864
[42] Fefferman, Charles, A note on spherical summation multipliers, Israel J. Math., 15, 44-52 (1973) · Zbl 0262.42007 · doi:10.1007/BF02771772
[43] Fefferman, Charles, Pointwise convergence of Fourier series, Ann. of Math. (2), 98, 551-571 (1973) · Zbl 0268.42009 · doi:10.2307/1970917
[44] Fefferman, Charles, Parabolic invariant theory in complex analysis, Adv. in Math., 31, 2, 131-262 (1979) · Zbl 0444.32013 · doi:10.1016/0001-8708(79)90025-2
[45] Fefferman, Charles, Selected theorems by Eli Stein. Essays on Fourier analysis in honor of Elias M. Stein, Princeton, NJ, 1991, Princeton Math. Ser. 42, 1-35 (1995), Princeton Univ. Press, Princeton, NJ · Zbl 0865.42001
[46] Fefferman, C. L.; Kohn, J. J., Estimates of kernels on three-dimensional CR manifolds, Rev. Mat. Iberoamericana, 4, 3-4, 355-405 (1988) · Zbl 0696.32009 · doi:10.4171/RMI/78
[47] Fefferman, Charles L.; Kohn, Joseph J., H\"{o}lder estimates on domains of complex dimension two and on three-dimensional CR manifolds, Adv. in Math., 69, 2, 223-303 (1988) · Zbl 0649.35068 · doi:10.1016/0001-8708(88)90002-3
[48] Fefferman, C.; Phong, D. H., Subelliptic eigenvalue problems. Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II, Chicago, Ill., 1981, Wadsworth Math. Ser., 590-606 (1983), Wadsworth, Belmont, CA · Zbl 0503.35071
[49] Fefferman, Charles L.; S\'{a}nchez-Calle, Antonio, Fundamental solutions for second order subelliptic operators, Ann. of Math. (2), 124, 2, 247-272 (1986) · Zbl 0613.35002 · doi:10.2307/1971278
[50] Gelfand, I. M.; Neumark, M. A., Unit\"{a}re Darstellungen der klassischen Gruppen, XL+333 pp. (1957), Akademie-Verlag, Berlin · Zbl 0077.03405
[51] Guillemin, V.; Uhlmann, G., Oscillatory integrals with singular symbols, Duke Math. J., 48, 1, 251-267 (1981) · Zbl 0462.58030
[52] Greenblatt, Michael, Sharp \(L^2\) estimates for one-dimensional oscillatory integral operators with \(C^\infty\) phase, Amer. J. Math., 127, 3, 659-695 (2005) · Zbl 1082.42009
[53] Greenleaf, Allan; Pramanik, Malabika; Tang, Wan, Oscillatory integral operators with homogeneous polynomial phases in several variables, J. Funct. Anal., 244, 2, 444-487 (2007) · Zbl 1127.35090 · doi:10.1016/j.jfa.2006.11.005
[54] Greenleaf, Allan; Seeger, Andreas, Oscillatory and Fourier integral operators with degenerate canonical relations, Publ. Mat.. Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations (El Escorial, 2000), Vol. Extra, 93-141 (2002) · Zbl 1024.42006 · doi:10.5565/PUBLMAT\_Esco02\_05
[55] Greenleaf, Allan; Seeger, Andreas, Oscillatory integral operators with low-order degeneracies, Duke Math. J., 112, 3, 397-420 (2002) · Zbl 1033.35164 · doi:10.1215/S0012-9074-02-11231-9
[56] Greenleaf, Allan; Uhlmann, Gunther, Estimates for singular Radon transforms and pseudodifferential operators with singular symbols, J. Funct. Anal., 89, 1, 202-232 (1990) · Zbl 0717.44001 · doi:10.1016/0022-1236(90)90011-9
[57] Gressman, Philip T., Uniform estimates for cubic oscillatory integrals, Indiana Univ. Math. J., 57, 7, 3419-3442 (2008) · Zbl 1187.42007 · doi:10.1512/iumj.2008.57.3403
[58] Gressman, Philip T.; Xiao, Lechao, Maximal decay inequalities for trilinear oscillatory integrals of convolution type, J. Funct. Anal., 271, 12, 3695-3726 (2016) · Zbl 1350.42025 · doi:10.1016/j.jfa.2016.09.003
[59] S. Guo, J. Roos, and P.-L. Yung, Sharp variation-norm estimates for oscillatory integrals related to Carleson’s theorem, arXiv:1710.10988 (2017). · Zbl 1452.42010
[60] Guo, Shaoming; Pierce, Lillian B.; Roos, Joris; Yung, Po-Lam, Polynomial Carleson operators along monomial curves in the plane, J. Geom. Anal., 27, 4, 2977-3012 (2017) · Zbl 1388.42040 · doi:10.1007/s12220-017-9790-7
[61] Henkin, G. M., Integral representation of functions which are holomorphic in strictly pseudoconvex regions, and some applications, Mat. Sb. (N.S.), 78 (120), 611-632 (1969) · Zbl 0206.09004
[62] Herz, Carl S., On the mean inversion of Fourier and Hankel transforms, Proc. Nat. Acad. Sci. U.S.A., 40, 996-999 (1954) · Zbl 0059.09901 · doi:10.1073/pnas.40.10.996
[63] Hirschman, I. I., Jr., On multiplier transformations, Duke Math. J., 26, 221-242 (1959) · Zbl 0085.09201
[64] Hirschman, I. I., Jr., Multiplier transformations. II, Duke Math. J., 28, 45-56 (1961) · Zbl 0095.08702
[65] H\"{o}rmander, Lars, Notions of convexity, Progress in Mathematics 127, viii+414 pp. (1994), Birkh\"{a}user Boston, Inc., Boston, MA · Zbl 0835.32001
[66] Hughes, Kevin, The discrete spherical averages over a family of sparse sequences, J. Anal. Math., 138, 1, 1-21 (2019) · Zbl 1423.42035 · doi:10.1007/s11854-019-0020-z
[67] Hunt, Richard A., On the convergence of Fourier series. Orthogonal Expansions and their Continuous Analogues, Proc. Conf., Edwardsville, Ill., 1967, 235-255 (1968), Southern Illinois Univ. Press, Carbondale, Ill. · Zbl 0159.35701
[68] Ikromov, Isroil A.; Kempe, Michael; M\"{u}ller, Detlef, Estimates for maximal functions associated with hypersurfaces in \(\mathbb{R}^3\) and related problems of harmonic analysis, Acta Math., 204, 2, 151-271 (2010) · Zbl 1223.42011 · doi:10.1007/s11511-010-0047-6
[69] Ionescu, Alexandru D., An endpoint estimate for the Kunze-Stein phenomenon and related maximal operators, Ann. of Math. (2), 152, 1, 259-275 (2000) · Zbl 0970.43002 · doi:10.2307/2661383
[70] Ionescu, Alexandru D., An endpoint estimate for the discrete spherical maximal function, Proc. Amer. Math. Soc., 132, 5, 1411-1417 (2004) · Zbl 1076.42014 · doi:10.1090/S0002-9939-03-07207-1
[71] Ionescu, Alexandru D., Rearrangement inequalities on semisimple Lie groups, Math. Ann., 332, 4, 739-758 (2005) · Zbl 1071.22013 · doi:10.1007/s00208-005-0650-6
[72] Ionescu, Alexandru D.; Magyar, Akos; Wainger, Stephen, Averages along polynomial sequences in discrete nilpotent Lie groups: singular Radon transforms. Advances in analysis: the legacy of Elias M. Stein, Princeton Math. Ser. 50, 146-188 (2014), Princeton Univ. Press, Princeton, NJ · Zbl 1302.43004
[73] Ionescu, Alexandru D.; Wainger, Stephen, \(L^p\) boundedness of discrete singular Radon transforms, J. Amer. Math. Soc., 19, 2, 357-383 (2006) · Zbl 1158.42007 · doi:10.1090/S0894-0347-05-00508-4
[74] B. Jessen, J. Marcinkiewicz, and A. Zygmund, Note on the differentiability of multiple integrals, Fund. Math. 25 (1935), 217-234. · JFM 61.0255.01
[75] Jones, Roger L.; Seeger, Andreas; Wright, James, Strong variational and jump inequalities in harmonic analysis, Trans. Amer. Math. Soc., 360, 12, 6711-6742 (2008) · Zbl 1159.42013 · doi:10.1090/S0002-9947-08-04538-8
[76] V. N. Karpushkin, A theorem concerning uniform estimates of oscillatory integrals when the phase is a function of two variables, J. Soviet Math. 35 (1986) 2809-2826. · Zbl 0602.58043
[77] Kesler, Robert; Lacey, Michael T.; Mena, Dar\'{\i}o, Sparse bounds for the discrete spherical maximal functions, Pure Appl. Anal., 2, 1, 75-92 (2020) · Zbl 1460.42027 · doi:10.2140/paa.2020.2.75
[78] Koenig, Kenneth D., On maximal Sobolev and H\"{o}lder estimates for the tangential Cauchy-Riemann operator and boundary Laplacian, Amer. J. Math., 124, 1, 129-197 (2002) · Zbl 1014.32031
[79] A. Kolmogorov, Une s\'erie de Fourier-Lebesgue divergente presque partout, Fund. Math. 4 (1923), 324-328. · JFM 49.0205.02
[80] K\"{o}rner, T. W., Fourier analysis, xii+591 pp. (1988), Cambridge University Press, Cambridge · Zbl 0649.42001 · doi:10.1017/CBO9781107049949
[81] Lacey, Michael; Thiele, Christoph, A proof of boundedness of the Carleson operator, Math. Res. Lett., 7, 4, 361-370 (2000) · Zbl 0966.42009 · doi:10.4310/MRL.2000.v7.n4.a1
[82] Lie, Victor, The (weak-\(L^2)\) boundedness of the quadratic Carleson operator, Geom. Funct. Anal., 19, 2, 457-497 (2009) · Zbl 1178.42007 · doi:10.1007/s00039-009-0010-x
[83] V. Lie, A note on the polynomial Carleson operator in higher dimensions, arXiv:1712.03092 (2017).
[84] Luzin, N. N., Integral i trigonometri\v{c}eski\u{\i} ryad, 550 pp. (1951), Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad
[85] Machedon, Matei, Estimates for the parametrix of the Kohn Laplacian on certain domains, Invent. Math., 91, 2, 339-364 (1988) · Zbl 0651.35017 · doi:10.1007/BF01389371
[86] Magyar, Akos, \(L^p\)-bounds for spherical maximal operators on \(\mathbf{Z}^n\), Rev. Mat. Iberoamericana, 13, 2, 307-317 (1997) · Zbl 0893.42011 · doi:10.4171/RMI/222
[87] Mauceri, Giancarlo, Zonal multipliers on the Heisenberg group, Pacific J. Math., 95, 1, 143-159 (1981) · Zbl 0474.43009
[88] McNeal, Jeffery D., Boundary behavior of the Bergman kernel function in \({\bf C}^2\), Duke Math. J., 58, 2, 499-512 (1989) · Zbl 0675.32020 · doi:10.1215/S0012-7094-89-05822-5
[89] Mirek, Mariusz, Square function estimates for discrete Radon transforms, Anal. PDE, 11, 3, 583-608 (2018) · Zbl 1383.42014 · doi:10.2140/apde.2018.11.583
[90] M\"{u}ller, Detlef, A geometric bound for maximal functions associated to convex bodies, Pacific J. Math., 142, 2, 297-312 (1990) · Zbl 0728.42015
[91] Nagel, Alexander; Rivi\`ere, N\'{e}stor; Wainger, Stephen, On Hilbert transforms along curves, Bull. Amer. Math. Soc., 80, 106-108 (1974) · Zbl 0293.44002 · doi:10.1090/S0002-9904-1974-13374-4
[92] Nagel, Alexander; Riviere, Nestor; Wainger, Stephen, A maximal function associated to the curve \((t, t^2)\), Proc. Nat. Acad. Sci. U.S.A., 73, 5, 1416-1417 (1976) · Zbl 0325.43009 · doi:10.1073/pnas.73.5.1416
[93] Nagel, Alexander; Rivi\`ere, N\'{e}stor M.; Wainger, Stephen, On Hilbert transforms along curves. II, Amer. J. Math., 98, 2, 395-403 (1976) · Zbl 0334.44012 · doi:10.2307/2373893
[94] Nagel, Alexander; Wainger, Stephen, \(L^2\) boundedness of Hilbert transforms along surfaces and convolution operators homogeneous with respect to a multiple parameter group, Amer. J. Math., 99, 4, 761-785 (1977) · Zbl 0374.44003 · doi:10.2307/2373864
[95] Nazarov, F.; Treil, S.; Volberg, A., The \(Tb\)-theorem on non-homogeneous spaces, Acta Math., 190, 2, 151-239 (2003) · Zbl 1065.42014 · doi:10.1007/BF02392690
[96] Oberlin, Daniel M., Two discrete fractional integrals, Math. Res. Lett., 8, 1-2, 1-6 (2001) · Zbl 0994.42010 · doi:10.4310/MRL.2001.v8.n1.a1
[97] Phong, D. H., On integral representations for the Neumann operator, Proc. Nat. Acad. Sci. U.S.A., 76, 4, 1554-1558 (1979) · Zbl 0402.35074 · doi:10.1073/pnas.76.4.1554
[98] Pierce, Lillian B., On discrete fractional integral operators and mean values of Weyl sums, Bull. Lond. Math. Soc., 43, 3, 597-612 (2011) · Zbl 1222.42021 · doi:10.1112/blms/bdq127
[99] Pierce, Lillian B., Discrete fractional Radon transforms and quadratic forms, Duke Math. J., 161, 1, 69-106 (2012) · Zbl 1246.44002 · doi:10.1215/00127094-1507288
[100] Pierce, Lillian B.; Yung, Po-Lam, A polynomial Carleson operator along the paraboloid, Rev. Mat. Iberoam., 35, 2, 339-422 (2019) · Zbl 1423.42031 · doi:10.4171/rmi/1057
[101] Range, R. Michael, Holomorphic functions and integral representations in several complex variables, Graduate Texts in Mathematics 108, xx+386 pp. (1986), Springer-Verlag, New York · Zbl 0591.32002 · doi:10.1007/978-1-4757-1918-5
[102] Rychkov, Vyacheslav S., Sharp \(L^2\) bounds for oscillatory integral operators with \(C^\infty\) phases, Math. Z., 236, 3, 461-489 (2001) · Zbl 0998.42002 · doi:10.1007/PL00004838
[103] Seeger, Andreas, Radon transforms and finite type conditions, J. Amer. Math. Soc., 11, 4, 869-897 (1998) · Zbl 0907.35147 · doi:10.1090/S0894-0347-98-00280-X
[104] Sj\"{o}lin, Per, Convergence almost everywhere of certain singular integrals and multiple Fourier series, Ark. Mat., 9, 65-90 (1971) · Zbl 0212.41703 · doi:10.1007/BF02383638
[105] Sogge, Christopher D., Concerning the \(L^p\) norm of spectral clusters for second-order elliptic operators on compact manifolds, J. Funct. Anal., 77, 1, 123-138 (1988) · Zbl 0641.46011 · doi:10.1016/0022-1236(88)90081-X
[106] Sogge, Christopher D., Propagation of singularities and maximal functions in the plane, Invent. Math., 104, 2, 349-376 (1991) · Zbl 0754.35004 · doi:10.1007/BF01245080
[107] Street, Brian, Multi-parameter Carnot-Carath\'{e}odory balls and the theorem of Frobenius, Rev. Mat. Iberoam., 27, 2, 645-732 (2011) · Zbl 1222.53036 · doi:10.4171/RMI/650
[108] Street, Brian, Multi-parameter singular Radon transforms I: The \(L^2\) theory, J. Anal. Math., 116, 83-162 (2012) · Zbl 1281.44003 · doi:10.1007/s11854-012-0004-8
[109] Strichartz, Robert S., Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J., 44, 3, 705-714 (1977) · Zbl 0372.35001
[110] Str\"{o}mberg, Jan-Olov, Weak type \(L^1\) estimates for maximal functions on noncompact symmetric spaces, Ann. of Math. (2), 114, 1, 115-126 (1981) · Zbl 0472.43010 · doi:10.2307/1971380
[111] Tao, Terence, The Bochner-Riesz conjecture implies the restriction conjecture, Duke Math. J., 96, 2, 363-375 (1999) · Zbl 0980.42006 · doi:10.1215/S0012-7094-99-09610-2
[112] Tao, Terence, Some recent progress on the restriction conjecture. Fourier analysis and convexity, Appl. Numer. Harmon. Anal., 217-243 (2004), Birkh\"{a}user Boston, Boston, MA · Zbl 1083.42008 · doi:10.1198/106186003321335099
[113] Tao, Terence; Wright, James, \(L^p\) improving bounds for averages along curves, J. Amer. Math. Soc., 16, 3, 605-638 (2003) · Zbl 1080.42007 · doi:10.1090/S0894-0347-03-00420-X
[114] Tolsa, Xavier, Analytic capacity, the Cauchy transform, and non-homogeneous Calder\'{o}n-Zygmund theory, Progress in Mathematics 307, xiv+396 pp. (2014), Birkh\"{a}user/Springer, Cham · Zbl 1290.42002 · doi:10.1007/978-3-319-00596-6
[115] Tomas, Peter A., A restriction theorem for the Fourier transform, Bull. Amer. Math. Soc., 81, 477-478 (1975) · Zbl 0298.42011 · doi:10.1090/S0002-9904-1975-13790-6
[116] Tomas, Peter A., Restriction theorems for the Fourier transform. Harmonic analysis in Euclidean spaces, Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978, Proc. Sympos. Pure Math., XXXV, Part, 111-114 (1979), Amer. Math. Soc., Providence, R.I. · Zbl 0506.42020
[117] Var\v{c}enko, A. N., Newton polyhedra and estimates of oscillatory integrals, Funkcional. Anal. i Prilo\v{z}en., 10, 3, 13-38 (1976)
[118] P. Zorin-Kranich, Maximal polynomial modulations of singular integrals, arXiv:1711. 03524 (2017). · Zbl 1467.42024
[119] Zygmund, A., Trigonometric series: Vols. I, II, Second edition, reprinted with corrections and some additions, Vol. I. xiv+383 pp.; Vol. II: vii+364 pp. (two volumes bound as one) pp. (1968), Cambridge University Press, London-New York
[120] Zygmund, A., On Fourier coefficients and transforms of functions of two variables, Studia Math., 50, 189-201 (1974) · Zbl 0278.42005 · doi:10.4064/sm-50-2-189-201
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.