Journal ArticleDOI
Harmonic analysis on product spaces
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The strong maximal operator which commutes with the p31382 is defined by as mentioned in this paper, which is related to many problems in the theory of multiple Fourier integrals (see Zygmund [21]).Abstract:
Rn x R' and commute with the dilations p33 '8(x2, x2) = (61x1, 62x2) for x1 E Rn, x2 E Rm, and 61, 82 > 0, then the corresponding operators are related to many problems in the theory of multiple Fourier integrals (see Zygmund [21]). The maximal operator which commutes with the p31382 is the Jessen, Marcinkiewicz, and Zygmund [14] strong maximal operator Ms defined by 1 Ms(f)(x1, x2) = sup RI A|(Y1, Y2)1 dy1 dy2 (xl, X2)GR JR1read more
Citations
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Weighted norm inequalities for the continuous square function
TL;DR: In this article, weighted norm inequalities for real-variable analogues of the Lusin area function were proved for singular integral operators and weighted Sobolev inequalities for degenerate Schrodinger operators.
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Characterizations of bounded mean oscillation on the polydisk in terms of Hankel operators and Carleson measures
Sarah H. Ferguson,Cora Sadosky +1 more
TL;DR: Chang and Fefferman as discussed by the authors describe two other BMO spaces, one contained in and the other containing product BMO, in terms of Carleson measures and Hankel operators, which play a significant role in harmonic analysis of the polydisk and in multivariable operator theory.
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Two problems of Calderón-Zygmund theory on product-spaces
TL;DR: In this paper, the conditions générales d'utilisation (http://www.numdam.org/conditions) are defined, i.e., toute utilisation commerciale ou impression systématique is constitutive d'une infraction pénale.
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Classes of singular integral operators along variable lines
Anthony Carbery,Anthony Carbery,Andreas Seeger,Andreas Seeger,Stephen Wainger,Stephen Wainger,James Wright +6 more
TL;DR: In this article, the main Lp estimates are proved by interpolating L2 bounds with suitable bounds in Hardy spaces on product domains, using almost-orthogonality arguments.
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Weighted anisotropic product Hardy spaces and boundedness of sublinear operators
TL;DR: In this paper, the authors characterized the weighted Lebesgue space Lpw(ℝn × ℝm) via the anisotropic Lusin-area function associated with A.
References
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Book
Singular Integrals and Differentiability Properties of Functions.
TL;DR: Stein's seminal work Real Analysis as mentioned in this paper is considered the most influential mathematics text in the last thirty-five years and has been widely used as a reference for many applications in the field of analysis.
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H p spaces of several variables
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On the existence of certain singular integrals
A. P. Calderón,A. Zygmund +1 more
TL;DR: In this article, it was shown that the integral can exist almost everywhere even if K is not integrable, and the most interesting special case is that of K (x) = 1/x.