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2012 Endpoint Estimate for Parametrized Littlewood-Paley Operator
F. Gao, Y. Lin, Z. Liu
Commun. Math. Anal. 12(2): 11-25 (2012).


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 $1<p<\infty$.


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F. Gao. Y. Lin. Z. Liu. "Endpoint Estimate for Parametrized Littlewood-Paley Operator." Commun. Math. Anal. 12 (2) 11 - 25, 2012.


Published: 2012
First available in Project Euclid: 16 March 2012

zbMATH: 1261.42012
MathSciNet: MR2905128

Primary: 42B20

Keywords: $L^p$ boundedness , logarithmic type Lipschitz condition , parametrized Littlewood-Paley operator

Rights: Copyright © 2012 Mathematical Research Publishers

Vol.12 • No. 2 • 2012
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