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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2007; 44(3): 733-745

Printed May 1, 2007

Copyright © The Korean Mathematical Society.

${\mathbf L}^{\bf p}$ bounds for the parabolic Marcinkiewicz integral with rough kernels

Yanping Chen and Yong Ding

Beijing Normal University, Beijing Normal University

Abstract

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We prove the $L^p\, (1 < p < \infty)$ boundedness of the parabolic Marcinkiewicz integral with the kernel function $\Omega\in
L(\log^+L)^{1/2}(S^{n-1}).$ The result is an improvement and extension of some known results.

Keywords: parabolic Marcinkiewicz integrals, mixed homogeneity space, rough kernel

MSC numbers: 42B20, 42B25

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