Communications in Mathematical Analysis

Endpoint Estimate for Parametrized Littlewood-Paley Operator

F. Gao, Y. Lin, and Z. Liu

Full-text: Open access

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 $1<p<\infty$.

Article information

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

Dates
First available in Project Euclid: 16 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.cma/1331929868

Mathematical Reviews number (MathSciNet)
MR2905128

Zentralblatt MATH identifier
1261.42012

Subjects
Primary: 42B20

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

Citation

Lin, Y.; Liu, Z.; Gao, F. Endpoint Estimate for Parametrized Littlewood-Paley Operator. Commun. Math. Anal. 12 (2012), no. 2, 11--25. https://projecteuclid.org/euclid.cma/1331929868


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