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2007 A rough multiple Marcinkiewicz integral along continuous surfaces
Huoxiong Wu
Tohoku Math. J. (2) 59(2): 145-166 (2007). DOI: 10.2748/tmj/1182180732

Abstract

By means of the method of block decompositions for kernel functions and some delicate estimates on Fourier transforms, the $L^p(\boldsymbol{R}^m\times\boldsymbol{R}^n\times\boldsymbol{R})$-boundedness of the multiple Marcinkiewicz integral is established along a continuous surface with rough kernel for some $p>1$. The condition on the integral kernel is the best possible for the $L^2$-boundedness of the multiple Marcinkiewicz integral operator.

Citation

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Huoxiong Wu. "A rough multiple Marcinkiewicz integral along continuous surfaces." Tohoku Math. J. (2) 59 (2) 145 - 166, 2007. https://doi.org/10.2748/tmj/1182180732

Information

Published: 2007
First available in Project Euclid: 18 June 2007

zbMATH: 1132.42007
MathSciNet: MR2347419
Digital Object Identifier: 10.2748/tmj/1182180732

Subjects:
Primary: 42B20
Secondary: 42B25, 42B99

Rights: Copyright © 2007 Tohoku University

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Vol.59 • No. 2 • 2007
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