Displaying similar documents to “On multilinear singular integrals of Calderón-Zygmund type.”

Multilinear singular integrals.

Christoph M. Thiele (2002)

Publicacions Matemàtiques

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We survey the theory of multilinear singular integral operators with modulation symmetry. The basic example for this theory is the bilinear Hilbert transform and its multilinear variants. We outline a proof of boundedness of Carleson's operator which shows the close connection of this operator to multilinear singular integrals. We discuss particular multilinear singular integrals which historically arose in the study of eigenfunctions of Schrödinger operators. ...

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...

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.

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.

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].

Multilinear almost diagonal estimates and applications

Árpád Bényi, Nikolaos Tzirakis (2004)

Studia Mathematica

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We prove that an almost diagonal condition on the (m + 1)-linear tensor associated to an m-linear operator implies boundedness of the operator on products of classical function spaces. We then provide applications to the study of certain singular integral operators.

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.