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Received: 2007-03-02

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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.12 P.2037-2040


A note on the Marcinkiewicz integral operators on Fpα,q

Author(s):  ZHANG Chun-jie, QIAN Rui-rui

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   purezhang@zju.edu.cn

Key Words:  Marcinkiewicz integral, Triebel-Lizorkin spaces, Fourier transforms

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ZHANG Chun-jie, QIAN Rui-rui. A note on the Marcinkiewicz integral operators on Fpα,q[J]. Journal of Zhejiang University Science A, 2007, 8(12): 2037-2040.

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A1 - ZHANG Chun-jie
A1 - QIAN Rui-rui
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DOI - 10.1631/jzus.2007.A2037

In this paper, we shall prove that the marcinkiewicz integral operator μΩ, when its kernel Ω satisfies the L1-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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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