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Weighted norm inequalities for the conjugate function and Hilbert transform. (English) Zbl 0262.44004

MSC:
44A15 Special integral transforms (Legendre, Hilbert, etc.)
26A45 Functions of bounded variation, generalizations
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[1] A. Benedek and R. Panzone, Continuity properties of the Hilbert transform, J. Functional Analysis 7 (1971), 217 – 234. · Zbl 0207.11201
[2] Charles Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), 587 – 588. · Zbl 0229.46051
[3] C. Fefferman and E. M. Stein, \?^\? spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137 – 193. · Zbl 0257.46078 · doi:10.1007/BF02392215 · doi.org
[4] Frank Forelli, The Marcel Riesz theorem on conjugate functions, Trans. Amer. Math. Soc. 106 (1963), 369 – 390. · Zbl 0121.09802
[5] V. F. Gapoškin, A generalization of the theorem of M. Riesz on conjugate functions., Mat. Sb. N. S. 46(88) (1958), 359 – 372 (Russian). · Zbl 0084.06305
[6] G. H. Hardy and J. E. Littlewood, Some more theorems concerning Fourier series and Fourier power series, Duke Math. J. 2 (1936), no. 2, 354 – 382. · Zbl 0014.21402 · doi:10.1215/S0012-7094-36-00228-4 · doi.org
[7] Henry Helson and Gabor Szegö, A problem in prediction theory, Ann. Mat. Pura Appl. (4) 51 (1960), 107 – 138. · Zbl 0178.50002 · doi:10.1007/BF02410947 · doi.org
[8] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415 – 426. · Zbl 0102.04302 · doi:10.1002/cpa.3160140317 · doi.org
[9] Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207 – 226. · Zbl 0236.26016
[10] Benjamin Muckenhoupt, Poisson integrals for Hermite and Laguerre expansions, Trans. Amer. Math. Soc. 139 (1969), 231 – 242. · Zbl 0175.12602
[11] Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. · Zbl 0207.13501
[12] Harold Widom, Singular integral equations in \?_\?, Trans. Amer. Math. Soc. 97 (1960), 131 – 160. · Zbl 0109.33002
[13] A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. · Zbl 0085.05601
[14] Marvin Rosenblum, Summability of Fourier series in \?^\?(\?\?), Trans. Amer. Math. Soc. 105 (1962), 32 – 42. · Zbl 0113.27602
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