×

Bilateral scales of Hardy inequalities and their applications to some problems of mathematical physics. (English. Russian original) Zbl 1374.26051

J. Math. Sci., New York 201, No. 6, 751-795 (2014); translation from Sovrem. Mat., Fundam. Napravl. 46, 49-91 (2012).

MSC:

26D15 Inequalities for sums, series and integrals
Full Text: DOI

References:

[1] I. A. Borovikov, “Some decompositions of the Sobolev spaces and their applications,” Vestn. Mosk. Energ. Inst., 6, 25-41 (2005).
[2] I. A. Borovikov, “Irrotational and solenoidal fields in the spaces <Emphasis Type=”Italic“>W <Emphasis Type=”Italic“>p <Emphasis Type=”Italic“>m,” Dokl. Math., 78, No. 2, 647-650 (2008). · Zbl 1185.46023 · doi:10.1134/S1064562408050013
[3] I. A. Borovikov, “Operators grad<Emphasis Type=”Italic“>, div<Emphasis Type=”Italic“>, rot<Emphasis Type=”Italic“>, and a generalization of H.Weyl theorem,” Vestn. Mosk. Energ. Inst., 6, 73-98 (2010).
[4] I. A. Borovikov and Yu.A. Dubinskii, “Decompositions of the Sobolev-Clifford modules and nonlinear variational problems,” Proc. Steklov Inst. Math., 260, 50-67 (2008). · Zbl 1233.46003 · doi:10.1134/S0081543808010057
[5] Yu.A. Dubinskii, “Decomposition of the spaces <Emphasis Type=”Italic“>W <Emphasis Type=”Italic“>p <Emphasis Type=”Italic“>m and <Emphasis Type=”Italic“>D <Emphasis Type=”Italic“>p <Emphasis Type=”Italic“>m,<Emphasis Type=”Italic“>k into sums of solenoidal and potential subspaces and factorization inequalities,” Dokl. Math., 73, No. 3, 349-353 (2006). · Zbl 1327.46035 · doi:10.1134/S1064562406030094
[6] Yu.A. Dubinskii, “Decomposition of the Sobolev scale and gradient-divergence scale into the sum of solenoidal and potential subspaces,” Proc. Steklov Inst. Math., 255, No. 1, 127-135 (2008). · Zbl 1349.46036 · doi:10.1134/S0081543806040109
[7] Yu.A. Dubinskii, “Hardy inequalities with exceptional parameter values and applications,” Dokl. Math., 80, No. 1, 558-562 (2009). · Zbl 1185.26042 · doi:10.1134/S1064562409040279
[8] Yu.A. Dubinskii, “On a scale of Hardy-type integral inequalities,” Dokl. Math., 81, No. 1, 111-114 (2010). · Zbl 1213.26024 · doi:10.1134/S106456241001031X
[9] Yu.A. Dubinskii, “On some weight functions in Hardy-type inequalities,” Vestn. Mosk. Energ. Inst., 6, 13-18 (2010).
[10] Yu.A. Dubinskii, “A Hardy-type inequality and its applications,” Proc. Steklov Inst. Math., 269, 106-126 (2010). · Zbl 1222.26027 · doi:10.1134/S0081543810020094
[11] Yu.A. Dubinskii, “On the choice of weight functions in Hardy-type inequalities,” Dokl. Math., 83, No. 2, 177-181 (2011). · Zbl 1273.26024 · doi:10.1134/S1064562411020153
[12] G. H. Hardy, D. E. Littlewood, and G. Pòlya, Inequalities, Cambridge, Cambridge University Press (1988). · Zbl 0634.26008
[13] A. Kufner, L. Maligranda, and L. E. Persson, The Hardy Inequality: About Its History and Some Results, Pilsen (2007). · Zbl 1213.42001
[14] A. I. Noarov, “On the solvability of stationary Fokker-Planck equations close to the Laplace equation,” Differ. Equ., 42, No. 4, 556-566 (2006). · Zbl 1154.35024 · doi:10.1134/S0012266106040124
[15] A. I. Noarov, “Generalized solvability of the stationary Fokker-Planck equation,” Differ. Equ., 43, No. 6, 833-839 (2007). · Zbl 1149.35020 · doi:10.1134/S0012266107060092
[16] A. I. Noarov, “Unique solvability of the stationary Fokker-Planck equation in a class of positive functions,” Differ. Equ., 45, No. 2, 197-208 (2009). · Zbl 1176.35175 · doi:10.1134/S0012266109020062
[17] B. Opic and A. Kufner, Hardy-Type Inequalities, Longman, Harlow (1990). · Zbl 0698.26007
[18] V. I. Smirnov, A Course of Higher Mathematics. Vol. 5, Pergamon Press, Reading, Mass. (1964). · Zbl 0122.29703
[19] R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, Am. Math. Soc. (2001). · Zbl 0981.35001
[20] H. Weyl, “The method of orthogonal projection in potential theory,” Duke Math. J., 7, 411-444 (1940). · Zbl 0026.02001 · doi:10.1215/S0012-7094-40-00725-6
[21] Library of Mathematical Guidebooks. Functional Analysis [in Russian], Nauka, Moscow (1974).
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.