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${\rm H^p}$ Bounds for Some Littlewood-Paley Operators with Rough Variable Kernels

Volume 8, Number 1 (2009), 16 - 27

${\rm H^p}$ Bounds for Some Littlewood-Paley Operators with Rough Variable Kernels

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Abstract

As a kind of Littlewood-Paley operator, the generalized parametric Marcinkiewicz integral operator $\mu_{\Omega}^\rho$ with rough variable kernel $\Omega$ and complex parameter $\rho$ has been considered in this article. The $H^p$ bounds for $\mu_{\Omega}^\rho$ are derived for $p=1$ and $01$ or $\rho=1$ or $\Omega$ is just a convolution-type kernel.