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2004 A class of multilinear oscillatory singular integrals related to block spaces
Shanzhen Lu, Huoxiong Wu
Tohoku Math. J. (2) 56(3): 299-315 (2004). DOI: 10.2748/tmj/1113246668

Abstract

This paper is devoted to the study on the $L^p$-mapping properties for a class of multilinear oscillatory singular integrals with polynomial phase and rough kernel. By means of the method of block decomposition for the kernel function, the authors show that for any non-trivial polynomial phase, the $L^p(\rz)$ boundedness of the multilinear oscillatory singular integral operators and that of the corresponding local multilinear singular integral operators are equivalent; and for any real-valued polynomial phase, the $L^p(\rz)$ boundedness of the multilinear oscillatory integral operators can be deduced from that of the corresponding multilinear singular integral operators.

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Shanzhen Lu. Huoxiong Wu. "A class of multilinear oscillatory singular integrals related to block spaces." Tohoku Math. J. (2) 56 (3) 299 - 315, 2004. https://doi.org/10.2748/tmj/1113246668

Information

Published: 2004
First available in Project Euclid: 11 April 2005

zbMATH: 1059.42012
MathSciNet: MR2075767
Digital Object Identifier: 10.2748/tmj/1113246668

Subjects:
Primary: 42B20

Rights: Copyright © 2004 Tohoku University

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Vol.56 • No. 3 • 2004
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