Generalizations of Calderón-Zygmund operators

Kôzô Yabuta

Displaying similar documents to “Generalizations of Calderón-Zygmund 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) = lím_ε→0 ∫_|x-y|>ε K(x-y) f(y) dy = p.v.K * f(x), where f belongs to some class of test functions.

Weighted norm inequalities for the geometric maximal operator.

David Cruz-Uribe, Christoph J. Neugebauer (1998)

Publicacions Matemàtiques

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Regularity properties of singular integral operators

Abdellah Youssfi (1996)

Studia Mathematica

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For s>0, we consider bounded linear operators from $D (ℝ^{n})$ into $D^{'} (ℝ^{n})$ whose kernels K satisfy the conditions $| \partial_{x}^{γ} K (x, y) | \leq C_{γ} {| x - y |}^{- n + s - | γ |}$ for x≠y, |γ|≤ [s]+1, $| \nabla_{y} \partial_{x}^{γ} K (x, y) | \leq C_{γ} {| x - y |}^{- n + s - | γ | - 1}$ for |γ|=[s], x≠y. We establish a new criterion for the boundedness of these operators from $L^{2} (ℝ^{n})$ into the homogeneous Sobolev space $Ḣ^{s} (ℝ^{n})$ . This is an extension of the well-known T(1) Theorem due to David and Journé. Our arguments make use of the function T(1) and the BMO-Sobolev space. We give some applications to the Besov and Triebel-Lizorkin spaces as well as some...

Fundamental solution, eigenvalue asymptotics and eigenfunctions of degenerate elliptic operators with positive potentials

Kazuhiro Kurata, Satoko Sugano (2000)

Studia Mathematica

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We show a weighted version of Fefferman-Phong's inequality and apply it to give an estimate of fundamental solutions, eigenvalue asymptotics and exponential decay of eigenfunctions for certain degenerate elliptic operators of second order with positive potentials.

On the two-weight problem for singular integral operators

David Cruz-Uribe, Carlos Pérez (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We give $A_{p}$ type conditions which are sufficient for two-weight, strong $(p, p)$ inequalities for Calderón-Zygmund operators, commutators, and the Littlewood-Paley square function $g_{λ}^{*}$ . Our results extend earlier work on weak $(p, p)$ inequalities in [13].

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 L^p, H^p 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...

On the inversion of pseudo-differential operators

Josefina Alonso (1979)

Studia Mathematica

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Some non-homogeneous symbols and associated pseudo-differential operators

S. Zaidman (1967)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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