Displaying similar documents to “Calderón-Zygmund operators on product spaces.”

Two problems of Calderón-Zygmund theory on product-spaces

Jean-Lin Journé (1988)

Annales de l'institut Fourier

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R. Fefferman has shown that, on a product-space with two factors, an operator T bounded on L 2 maps L ∞ into BMO of the product if the mean oscillation on a rectangle R of the image of a bounded function supported out of a multiple R’ of R, is dominated by C | R | s | R | - s , for some s > 0 . We show that this result does not extend in general to the case where E has three or more factors but remains true in this case if in addition T is a convolution operator, provided s > s 0 ( E ) . We also show that the Calderon-Coifman...

On multilinear singular integrals of Calderón-Zygmund type.

Loukas Grafakos, Rodolfo H. Torres (2002)

Publicacions Matemàtiques

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A variety of results regarding multilinear singular Calderón-Zygmund integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur's test, and a multilinear version of the T1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators....

Calderón-type reproducing formula and the Tb theorem.

Yong Sheng Han (1994)

Revista Matemática Iberoamericana

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In this paper we use the Calderón-Zygmund operator theory to prove a Calderón type reproducing formula associated with a para-accretive function. Using our Calderón-type reproducing formula we introduce a new class of the Besov and Triebel-Lizorkin spaces and prove a Tb theorem for these new spaces.

Fourier analysis in several parameters.

Robert Fefferman (1986)

Revista Matemática Iberoamericana

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Clearly, one of the most basic contributions to the fields of real variables, partial differential equations and Fourier analysis in recent times has been the celebrated theorem of Calderón and Zygmund on the boundedness of singular integrals on R [1].

Vector valued inequalities for strongly singular Calderón-Zygmund operators.

Josefina Alvarez, Mario Milman (1986)

Revista Matemática Iberoamericana

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In this article we consider a theory of vector valued strongly singular operators. Our results include Lp, Hp and BMO continuity results. Moreover, as is well known, vector valued estimates are closely related to weighted norm inequalities. These results are developed in the first four sections of our paper. In section 5 we use our vector valued singular integrals to estimate the corresponding maximal operators. Finally in section 6 we discuss...

Hardy space estimates for multilinear operators (I).

Ronald R. Coifman, Loukas Grafakos (1992)

Revista Matemática Iberoamericana

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In this article we study bilinear operators given by inner products of finite vectors of Calderón-Zygmund operators. We find that necessary and sufficient condition for these operators to map products of Hardy spaces into Hardy spaces is to have a certain number of moments vanishing and under this assumption we prove a Hölder-type inequality in the H space context.

The boundedness of Calderón-Zygmund operators on the spaces F .

Michel Frazier, Rodolfo Torres, Guido Weiss (1988)

Revista Matemática Iberoamericana

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Calderón-Zygmund operators are generalizations of the singular integral operators introduced by Calderón and Zygmund in the fifties [CZ]. These singular integrals are principal value convolutions of the form Tf(x) = límε→0 ∫|x-y|>ε K(x-y) f(y) dy = p.v.K * f(x), where f belongs to some class of test functions.