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On the functions of Littlewood-Paley, Lusin and Marcinkiewicz. (English) Zbl 0105.05104

Trans. Am. Math. Soc. 88, 430-466 (1958); Correction. ibid. 98, 186 (1961).

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[1] A. P. Calderón, On a theorem of Marcinkiewicz and Zygmund, Trans. Amer. Math. Soc. 68 (1950), 55 – 61. · Zbl 0035.18903
[2] A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85 – 139. · Zbl 0047.10201 · doi:10.1007/BF02392130
[3] A. P. Calderón and A. Zygmund, On singular integrals, Amer. J. Math. 78 (1956), 289 – 309. · Zbl 0072.11501 · doi:10.2307/2372517
[4] J. Horváth, Sur les fonctions conjuguées à plusieurs variables, Nederl. Akad. Wetensch. Proc. Ser. A. 56 = Indagationes Math. 15 (1953), 17 – 29 (French). · Zbl 0050.10501
[5] J. E. Littlewood and R. E. A. C. Paley, Theorems on Fourier series and power series, Part I, J. London Math. Soc. vol. 6 (1931) pp. 230-233; Part II, Proc. London Math. Soc. vol. 42 (1937) pp. 52-89; Part III, ibid, vol. 43 (1937) pp. 105-126. · Zbl 0002.18803
[6] N. Lusin, Sur une propriété des fonctions a carré sommable, Bull. Calcutta Math. Soc. vol. 20 (1930) pp. 139-154. · JFM 56.0969.01
[7] J. Marcinkiewicz, Sur quelques integrales de type de Dini, Annales de la Société Polonaise, vol. 17 (1938) pp. 42-50. · JFM 64.0225.03
[8] -, Sur les series de Fourier, Fund. Math. vol. 27 (1936) pp. 38-69. · Zbl 0014.21501
[9] J. Marcinkiewicz and A. Zygmund, A theorem of Lusin. Part I, Duke Math. J. 4 (1938), no. 3, 473 – 485. · Zbl 0019.42001 · doi:10.1215/S0012-7094-38-00440-5
[10] D. Waterman, On an integral of Marcinkiewicz, Proceedings of the International Congress of Mathematicians, vol. 2, 1954, pp. 185-186; also On functions analytic in a half-plane, Trans. Amer. Math. Soc. vol. 81 (1956) pp. 167-194.
[11] A. Zygmund, On certain integrals, Trans. Amer. Math. Soc. 55 (1944), 170 – 204. · Zbl 0061.13902
[12] A. Zygmund, Proof of a theorem of Littlewood and Paley, Bull. Amer. Math. Soc. 51 (1945), 439 – 446. · Zbl 0060.14703
[13] A. Zygmund, On a theorem of Marcinkiewicz concerning interpolation of operations, J. Math. Pures Appl. (9) 35 (1956), 223 – 248. · Zbl 0070.33701
[14] -, Trigonometrical series, 2d. ed., to appear. · Zbl 0011.01703
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