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Endpoint Estimate for Parametrized Littlewood-Paley Operator

Commun. Math. Anal.
Volume 12, Number 2 (2012), 11 - 25

Endpoint Estimate for Parametrized Littlewood-Paley Operator

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Abstract

In this paper, the authors obtain the $(L^1,L^{1,\infty})$ type boundedness for the parametrized Littlewood-Paley operator $\mu_\lambda^{*,\rho}$ with kernel satisfying the logarithmic type Lipschitz condition. Moreover, the $L^p(\mathbb{R}^{n})$ boundedness of the operator $\mu_\lambda^{*,\rho}$ can be deduced, where $1<p<\infty$.