Abstract
In the present paper, we study the integral properties of multidimensional Hilbert transforms.
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L. Zhizhiashvili, Trigonometric Fourier Series and Their Conjugates, Kluwer Acad. Publ., Dordrecht-Boston-London, 1996.
L. V. Zhizhiashvili, Some Questions of the Multidimensional Harmonic Analysis [in Russian], Tbilisi State Univ., Tbilisi, 1996.
A. Besicovitch, “Sur la nature des fonctions a carré sommable mésurables,” Fund. Math., 4 (1923), 172–195.
A. Besicovitch, “On a general metric property of summable functions,” J. Lond. Math. Soc., 1 (1926), 120–128.
E. Titchmarsh, Introduction to the Theory of Fourier Integrals, Second edition, Oxford Univ. Press, Oxford, 1948; Russian transl.: Gostekhizdat, Moscow-Leningrad, 1948.
A. Zygmund, Trigonometric Series, vol. 2, Cambridge Univ. Press, Cambridge, 1960; Russian transl.: Moscow, Mir, 1965.
J. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981; Russian transl.: Moscow, Nauka, 1984.
M. Riesz, “Les fonctions conjuguées et les series de Fourier,” Comp. Rend., 178 (1924), 1464–1467.
M. Riesz, “Sur les fonctions conjuguées,” Math. Z., 27 (1927), 218–244.
A. Zygmund, Intégrales Singularières, Lecture Notes in Math., vol. 204, Springer-Verlag, Berlin-Heidelberg-New York, 1971.
E. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, NJ, 1971; Russian transl.: Moscow, Mir, 1974.
H. Kober, “A note on Hilbert’s operator,” Bull. Amer. Math. Soc., 48 (1942), no. 1, 421–426.
H. Kober, “A note on Hilbert transforms,” J. Lond. Math. Soc., 18 (1943), no. 2, 66–71.
K. Sokol-Sokolowski, “On trigonometric series conjugate of Fourier series of two variables,” Fund. Math., 34 (1947), 166–182.
A. P. Calderón and A. Zygmund, “On the existence of certain singular integrals,” Acta Math., 88 (1952), no. 1–2, 85–139.
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Dedicated to S. M. Nikol’skii on the occasion of his 100th birthday
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Translated from Matematicheskie Zametki, vol. 80, no. 2, 2006, pp. 179–186.
Original Russian Text Copyright © 2006 by L. V. Zhizhiashvili.
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Zhizhiashvili, L.V. On some integral properties of multidimensional Hilbert operators. Math Notes 80, 175–182 (2006). https://doi.org/10.1007/s11006-006-0125-4
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DOI: https://doi.org/10.1007/s11006-006-0125-4