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On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz


Author: E. M. Stein
Journal: Trans. Amer. Math. Soc. 88 (1958), 430-466
MSC: Primary 26.00; Secondary 30.00
DOI: https://doi.org/10.1090/S0002-9947-1958-0112932-2
Correction: Trans. Amer. Math. Soc. 98 (1961), 186.
MathSciNet review: 0112932
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  • [1] A. P. Calderón, On the theorem of Marcinkiewicz and Zygmund, Trans. Amer. Math. Soc. vol. 68 (1950) pp. 55-61. MR 0032864 (11:357f)
  • [2] A. P. Calderón and A. Zygmund, On the existence of certain singular integrals, Acta Math. vol. 88 (1952) pp. 85-139. MR 0052553 (14:637f)
  • [3] -, On singular integrals, Amer. J. Math. vol. 78 (1956) pp. 289-309. MR 0084633 (18:894a)
  • [4] J. Horvàth, Sur les fonctions conjuguées a plusieurs variables, Nederl. Akad. Wetensch. vol. 15 (1953) pp. 17-29. MR 0053276 (14:747b)
  • [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.
  • [6] N. Lusin, Sur une propriété des fonctions a carré sommable, Bull. Calcutta Math. Soc. vol. 20 (1930) pp. 139-154.
  • [7] J. Marcinkiewicz, Sur quelques integrales de type de Dini, Annales de la Société Polonaise, vol. 17 (1938) pp. 42-50.
  • [8] -, Sur les series de Fourier, Fund. Math. vol. 27 (1936) pp. 38-69.
  • [9] J. Marcinkiewicz and A. Zygmund, On a theorem of Lusin, Duke Math. J. vol. 4 (1938) pp. 473-485. MR 1546069
  • [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. vol. 55 (1944) pp. 170-204. MR 0009966 (5:230b)
  • [12] -, Proof of a theorem of Littlewood and Paley, Bull. Amer. Math. Soc. vol. 51 (1945) pp. 439-446. MR 0012306 (7:8b)
  • [13] -, On a theorem of Marcinkiewicz concerning interpolation of operations, J. Math. Pures Appl. vol. 35 (1956) pp. 223-248. MR 0080887 (18:321d)
  • [14] -, Trigonometrical series, 2d. ed., to appear.

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DOI: https://doi.org/10.1090/S0002-9947-1958-0112932-2
Article copyright: © Copyright 1958 American Mathematical Society

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