×

zbMATH — the first resource for mathematics

Estimates for translation invariant operators in \(L^p\) spaces. (English) Zbl 0093.11402

PDF BibTeX XML Cite
Full Text: DOI
References:
[1] A. Beurling &H. Helson, Fourier-Stieltjes transforms with bounded powers.Math. Scand., 1 (1953), 120–126. · Zbl 0050.33004
[2] A. P. Calderón &A. Zygmund, On the existence of certain singular integrals.Acta Math., 88 (1952), 85–139. · Zbl 0047.10201 · doi:10.1007/BF02392130
[3] –, Algebras of certain singular operators.Amer. J. Math., 78 (1956), 310–320. · Zbl 0072.11601 · doi:10.2307/2372518
[4] H. Helson, Isomorphisms of abelian group algebras.Ark. Mat., 2 (1953), 475–487. · Zbl 0052.11802 · doi:10.1007/BF02591001
[5] J. E. Littlewood &R. E. A. C. Paley, Theorems on Fourier series and power series (II).Proc. London Math. Soc., 42 (1937), 52–89. · Zbl 0015.25402 · doi:10.1112/plms/s2-42.1.52
[6] L. H. Loomis,An introduction to abstract harmonic analysis. Toronto, New York, London 1953. · Zbl 0052.11701
[7] J. Marcinkiewicz, Sur les multiplicateurs des séries de Fourier.Studia Math., 8 (1939), 78–91. · Zbl 0020.35403
[8] S. G. Mihlin, On the multipliers of Fourier integrals.Dokl. Akad. Nauk SSSR (N. S.), 109 (1956), 701–703 (Russian.) · Zbl 0073.08402
[9] –, Fourier integrals and multiple singular integrals.Vestnik Leningrad. Univ. Ser. Mat. Mech. Astr., 12 (1957), No. 7, 143–155. (Russian.) · Zbl 0092.31701
[10] M. Riesz, Sur les functions conjuguées.Math. Z., 27 (1927), 218–244. · JFM 53.0259.02 · doi:10.1007/BF01171098
[11] –, Sur les maxima des formes bilinéaires et sur les fonctionnelles linéaires.Acta Math., 49 (1926), 465–497. · JFM 53.0259.03 · doi:10.1007/BF02564121
[12] L. Schwartz,Théorie des distributions I–II. Paris 1950–51. · Zbl 0037.07301
[13] –, Sur les multiplicateurs deF L p . Kungl. fysiogr. sällsk. i Lund förh., 22 (1952), 124–128.
[14] Yu. A. Šreider, The structure of maximal ideals in rings of measures with convolution.Amer. Math. Soc. Translation No 81, 1953. (Translated fromMat. Sbornik (N. S.), 27 (69) (1950), 297–318.)
[15] E. M. Stein, On the functions of Littlewood-Paley, Lusin and Marcinkiewicz.Trans. Amer. Math. Soc., 88 (1958), 430–466. · Zbl 0105.05104 · doi:10.1090/S0002-9947-1958-0112932-2
[16] G. O. Thorin, Convexity Theorems generalizing those of M. Riesz and Hadamard with some applications.Medd. Lunds Univ. Matem. Sem., 9 (1948). · Zbl 0034.20404
[17] A. Zygmund,Trigonometrical series I–II. London 1959. · Zbl 0085.05601
[18] , On a theorem of Marcinkiewicz concerning interpolation of operators.J. Math. Pures Appl., 35 (1956), 223–248. · Zbl 0070.33701
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.