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• [2] A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85–139. MR 0052553 (14,637f)
• [3] A. P. Calderón and A. Zygmund, On singular integrals, Amer. J. Math. 78 (1956), 289–309. MR 0084633 (18,894a)
• [4] J. Horváth, Sur les fonctions conjuguées à plusieurs variables, Nederl. Akad. Wetensch. Proc. Ser. A. 56 = Indagationes Math. 15 (1953), 17–29 (French). 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, A theorem of Lusin. Part I, Duke Math. J. 4 (1938), no. 3, 473–485. MR 1546069, http://dx.doi.org/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. MR 0009966 (5,230b), http://dx.doi.org/10.1090/S0002-9947-1944-0009966-5
• [12] A. Zygmund, Proof of a theorem of Littlewood and Paley, Bull. Amer. Math. Soc. 51 (1945), 439–446. MR 0012306 (7,8b), http://dx.doi.org/10.1090/S0002-9904-1945-08374-8
• [13] A. Zygmund, On a theorem of Marcinkiewicz concerning interpolation of operations, J. Math. Pures Appl. (9) 35 (1956), 223–248. MR 0080887 (18,321d)
• [14] -, Trigonometrical series, 2d. ed., to appear.

Bibliography

[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.