×

Banach function spaces and interpolation methods. I: The abstract theory. (English) Zbl 0292.46020


MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
43A15 \(L^p\)-spaces and other function spaces on groups, semigroups, etc.
Full Text: DOI

References:

[1] Aronszajn, N.; Gagliardo, E., Interpolation spaces and interpolation methods, Ann. Mat. Pura Appl., 68, 51-118 (1965) · Zbl 0195.13102
[2] Bennett, C., A Hausdorff-Young theorem for rearrangement-invariant spaces, Pacific J. Math., 47, 311-328 (1973) · Zbl 0242.42018
[3] Bennett, C., Banach function spaces and interpolation methods. II. Interpolation of weak-type operators, (Proc. Conf. on Linear Operators and Approximation. Proc. Conf. on Linear Operators and Approximation, Oberwolfach (1974), Birkhauser-Verlag), To appear in · Zbl 0303.46029
[4] C. BennettJ. Approx. Theory; C. BennettJ. Approx. Theory · Zbl 0311.42005
[5] Berens, H., Interpolationsmethoden zur Behandlung von Approximations-prozessen auf Banachräumen, (Lecture Notes No. 64 (1968), Springer Verlag: Springer Verlag Berlin) · Zbl 0164.43801
[6] Boyd, D. W., The Hilbert transform on rearrangement-invariant spaces, Canad. J. Math., 19, 599-616 (1967) · Zbl 0147.11302
[7] Boyd, D. W., Indices of function spaces and their relationship to interpolation, Canad. J. Math., 21, 1245-1254 (1969) · Zbl 0184.34802
[8] Butzer, P. L.; Berens, H., Semi-Groups of Operators and Approximation (1967), Springer-Verlag: Springer-Verlag New York · Zbl 0164.43702
[9] Calderón, A. P., Spaces between \(L^1\) and \(L^∞\) and the theorem of Marcinkiewicz, Studia Math., 26, 273-299 (1966) · Zbl 0149.09203
[10] Fehér, F.; Gaspar, D.; Johnen, H., Der Konjugiertenoperator auf rearrangement invarienten Funktionräumen, Math. Z., 134, 129-141 (1973) · Zbl 0265.46035
[11] Hardy, G. H.; Littlewood, J. E., Notes on the theory of series (XVIII): On the convergence of Fourier series, (Proc. Camb. Phil. Soc., 31 (1935)), 317-323 · Zbl 0012.35104
[12] Collected Papers, III, 425-431.; Collected Papers, III, 425-431.
[13] Lions, J.-L; Peetre, J., Sur une classe d’espaces d’interpolation, Inst. Hautes Etudes Sci. Publ. Math., 19, 5-68 (1964) · Zbl 0148.11403
[14] Lorentz, G. G.; Shimogaki, T., Interpolation theorems for operators in function spaces, J. Functional Analysis, 2, 31-51 (1968) · Zbl 0162.44504
[15] Lorentz, G. G.; Shimogaki, T., Interpolation theorems for the pairs of spaces \((L^p, L^∞)\) and \((L^1, L^q)\), Trans. Amer. Math. Soc., 159, 207-221 (1971) · Zbl 0244.46044
[16] Luxemburg, W. A.J, Banach function spaces, Thesis (1955), Delft · Zbl 0068.09204
[17] Luxemburg, W. A.J, Rearrangement-invariant Banach function spaces, (Queen’s Papers 10 (1967), Queen’s University), 83-144 · Zbl 0162.44701
[18] Luxemburg, W. A.J; Zaanen, A. C., Notes on Banach function spaces, I-V, Indag. Math., 25 (1963) · Zbl 0133.37204
[19] Luxemburg, W. A.J; Zaanen, A. C., Some examples of normed Köthe spaces, Math. Ann., 162, 337-350 (1966) · Zbl 0132.35002
[20] Peetre, J., Espaces d’interpolation, généralizations, applications, (Rend. Sem. Mat. Fis. Milano, 34 (1964)), 133-164 · Zbl 0151.17902
[21] Peetre, J., A Theorem of Interpolation of Normed Spaces, Notas Mat. No. 39 (1968) · Zbl 0162.44502
[22] Scherer, K., Über die Dualen von Banachräumen, Acta Math. Sci. Hung., 23, 343-365 (1972) · Zbl 0257.46027
[23] Shimogaki, T., Hardy-Littlewood majorants in function spaces, J. Math. Soc. Japan, 17, 365-373 (1965) · Zbl 0135.16304
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.