Continuity of Calderón-zygmund Operators

Continuity of Calderón-Zygmund Operators on the Space BMO

David and Journé discovered a criterion for the continuity on L of CalderónZygmund operators defined by singular integrals. In their approach the distributional kernel of the given operator is locally Hölder continuous outside the diagonal. The aim of this paper is to prove a David-Journé theorem where this smoothness assumption is replaced by a weaker one. Our approach strongly relies on an al...

Multilinear Calderón-zygmund Operators on Hardy Spaces

It is shown that multilinear Calderón-Zygmund operators are bounded on products of Hardy spaces.

Lp-continuity for Calderón–Zygmund operator

Abstract. Given a Calderón–Zygmund (C–Z for short) operator T , which satisfies Hörmander condition, we prove that: if T maps all the characteristic atoms to W L1, then T is continuous from Lp to Lp(1 < p < ∞). So the study of strong continuity on arbitrary function in Lp has been changed into the study of weak continuity on characteristic functions.

A Note on Calderón-zygmund Singular Integral Convolution Operators

Bilinear Square Functions and Vector-Valued Calderón-Zygmund Operators

Boundedness results for bilinear square functions and vector-valued operators on products of Lebesgue, Sobolev, and other spaces of smooth functions are presented. Bilinear vector-valued Calderón-Zygmund operators are introduced and used to obtain bounds for the optimal range of estimates in target Lebesgue spaces including exponents smaller than one.