A note on the Marcinkiewicz integral operators on F p

In this paper, we shall prove that the Marcinkiewicz integral operator mu Omega , when its kernel Omega satisfies the L -Dini condition, is bounded on the Triebel-Lizorkin spaces. It is well known that the Triebel-Lizorkin spaces are generalizations of many familiar spaces such as the Lebesgue space...

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Bibliographic Details
Published in:Journal of Zhejiang University. A. Science 2007-11, Vol.8 (12), p.2037-2040
Main Authors: Zhang, Chun-jie, Qian, Rui-rui
Format: Article
Language:English
Online Access:Get full text
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Summary:In this paper, we shall prove that the Marcinkiewicz integral operator mu Omega , when its kernel Omega satisfies the L -Dini condition, is bounded on the Triebel-Lizorkin spaces. It is well known that the Triebel-Lizorkin spaces are generalizations of many familiar spaces such as the Lebesgue spaces and the Sobolev spaces. Therefore, our result extends many known theorems on the Marcinkiewicz integral operator. Our method is to regard the Marcinkiewicz integral operator as a vector valued singular integral. We also use another characterization of the Triebel-Lizorkin space which makes our approach more clear.
ISSN:1673-565X
DOI:10.1631/jzus.2007.A2037