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February 2020 Sharp estimates for commutators of bilinear operators on Morrey type spaces
Dinghuai WANG, Jiang ZHOU, Zhidong TENG
Hokkaido Math. J. 49(1): 165-199 (February 2020). DOI: 10.14492/hokmj/1591085016

Abstract

Denote by $T$ and $I_{\alpha}$ the bilinear Calderón-Zygmund operators and bilinear fractional integrals, respectively. In this paper, it is proved that if $b_{1},b_{2}\in {\rm CMO}$ (the BMO-closure of $C^{\infty}_{c}(\mathbb{R}^n)$), $[\Pi \vec{b},T]$ and $[\Pi\vec{b},I_{\alpha}]$ $(\vec{b}=(b_{1},b_{2}))$ are all compact operators from $\mathcal{M}^{p_{0}}_{\vec{P}}$ (the norm of $\mathcal{M}^{p_{0}}_{\vec{P}}$ is strictly smaller than $2-$fold product of the Morrey norms) to $M^{q_{0}}_{q}$ for some suitable indices $p_{0},p_{1},p_{2}$ and $q_{0},q$. Specially, we also show that if $b_{1}=b_{2}$, then $b_{1}, b_{2}\in {\rm CMO}$ is necessary for the compactness of $[\Pi\vec{b},I_{\alpha}]$ on Morrey space.

Citation

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Dinghuai WANG. Jiang ZHOU. Zhidong TENG. "Sharp estimates for commutators of bilinear operators on Morrey type spaces." Hokkaido Math. J. 49 (1) 165 - 199, February 2020. https://doi.org/10.14492/hokmj/1591085016

Information

Published: February 2020
First available in Project Euclid: 2 June 2020

zbMATH: 07209524
MathSciNet: MR4105540
Digital Object Identifier: 10.14492/hokmj/1591085016

Subjects:
Primary: 42B20, 47B07
Secondary: 42B99, 47G99

Rights: Copyright © 2020 Hokkaido University, Department of Mathematics

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Vol.49 • No. 1 • February 2020
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