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WEIGHTED ESTIMATES FOR SINGULAR INTEGRAL OPERATORS WITH NONSMOOTH KERNELS AND APPLICATIONS

Part of: Harmonic analysis in several variables Abstract harmonic analysis General theory of linear operators

Published online by Cambridge University Press:  01 December 2008

GUOEN HU  and
DACHUN YANG
GUOEN HU
Affiliation:
Department of Applied Mathematics, University of Information Engineering, P.O. Box 1001-747, Zhengzhou 450002, People’s Republic of China (email: [email protected])
DACHUN YANG*
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People’s Republic of China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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Let 𝒳 be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, two weighted estimates related to weights are established for singular integral operators with nonsmooth kernels via a new sharp maximal operator associated with a generalized approximation to the identity. As applications, the weighted Lp(𝒳) and weighted endpoint estimates with general weights are obtained for singular integral operators with nonsmooth kernels, their commutators with BMO (𝒳) functions, and associated maximal operators. Some applications to holomorphic functional calculi of elliptic operators and Schrödinger operators are also presented.

Keywords

space of homogeneous typeapproximation to the identityweightnorm inequalitysingular integral operatormaximal operatornonsmooth kernel

MSC classification

Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory 47A30: Norms (inequalities, more than one norm, etc.) 43A99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 3 , December 2008 , pp. 377 - 417
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

The first author was supported by the NNSF (No. 10671210) of China and the second (corresponding) author was supported by National Science Foundation for Distinguished Young Scholars (No. 10425106) and NCET (No. 04-0142) of China.

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