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December 2018 Littlewood-Paley $g^{\ast}_{\lambda,\mu}$-function and Its Commutator on Non-homogeneous Generalized Morrey Spaces
Guanghui LU, Shaoxian MA, Miaomiao WANG
Tokyo J. Math. 41(2): 617-626 (December 2018). DOI: 10.3836/tjm/1502179247

Abstract

Let $\mu$ be a non-negative Radon measure on $\mathbb{R}^{d}$ which may be a non-doubling measure. In this paper, the authors prove that the Littlewood-Paley $g^{\ast}_{\lambda,\mu}$-function is bounded on the generalized Morrey space $\mathcal{L}^{p,\phi}(\mu)$, and also obtain that the commutator $g^{\ast}_{\lambda,\mu,b}$ generated by the Littlewood-Paley function $g^{\ast}_{\lambda,\mu}$ and the regular bounded mean oscillation space $(=$RBMO$)$, which is due to X. Tolsa, is bounded on $\mathcal{L}^{p,\phi}(\mu)$. As a corollary, the authors prove that the commutator $g^{\ast}_{\lambda,\mu,b}$ is bounded on the Morrey space $\mathcal{M}^{p}_{q}(\mu)$ defined by Sawano and Tanaka when we take $\phi(t)=t^{1-\frac{p}{q}}$ with $1<p<q<\infty$.

Citation

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Guanghui LU. Shaoxian MA. Miaomiao WANG. "Littlewood-Paley $g^{\ast}_{\lambda,\mu}$-function and Its Commutator on Non-homogeneous Generalized Morrey Spaces." Tokyo J. Math. 41 (2) 617 - 626, December 2018. https://doi.org/10.3836/tjm/1502179247

Information

Published: December 2018
First available in Project Euclid: 20 November 2017

zbMATH: 07053496
MathSciNet: MR3908814
Digital Object Identifier: 10.3836/tjm/1502179247

Subjects:
Primary: 42B25
Secondary: 42B35

Rights: Copyright © 2018 Publication Committee for the Tokyo Journal of Mathematics

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Vol.41 • No. 2 • December 2018
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