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# The Parabolic Littlewood--Paley Operator with Hardy Space Kernels

Published:2009-12-01
Printed: Dec 2009
• Yanping Chen
• Yong Ding
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## Abstract

In this paper, we give the $L^p$ boundedness for a class of parabolic Littlewood--Paley $g$-function with its kernel function $\Omega$ is in the Hardy space $H^1(S^{n-1})$.
 Keywords: parabolic Littlewood-Paley operator, Hardy space, rough kernel
 MSC Classifications: 42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.) 42B25 - Maximal functions, Littlewood-Paley theory

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