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August 2006 Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on classical Morrey spaces
Satoru SHIRAI
Hokkaido Math. J. 35(3): 683-696 (August 2006). DOI: 10.14492/hokmj/1285766424

Abstract

We prove that $b$ is in $BMO(\R^n)$ if and only if the commutator $[b,I_{\alpha}]$ of the multiplication operator by $b$ and the fractional integral operator $I_{\alpha}$ is bounded from the classical Morrey space $L^{p,\lambda}(\R^n)$ to $L^{q,\mu}(\R^n)$, where $1<p< \infty$, $0<\alpha <n$, $0<\lambda <n- \alpha p$, $1/q=1/p-\alpha /n$ and $\lambda /p = \mu /q$. Also we will show that $b$ is in $\dot{\Lambda}_{\beta}(\R^n)$ if and only if the commutator $[b,I_{\alpha}]$ is bounded from the classical Morrey space $L^{p,\lambda}(\R^n)$ to $L^{q,\mu}(\R^n)$ or from $L^{p,\lambda}(\R^n)$ to $L^{q,\lambda}(\R^n)$, where $\alpha$ and $\beta$ satisfy some conditions.

Citation

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Satoru SHIRAI. "Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on classical Morrey spaces." Hokkaido Math. J. 35 (3) 683 - 696, August 2006. https://doi.org/10.14492/hokmj/1285766424

Information

Published: August 2006
First available in Project Euclid: 29 September 2010

zbMATH: 1122.42007
MathSciNet: MR2275989
Digital Object Identifier: 10.14492/hokmj/1285766424

Subjects:
Primary: 42B25
Secondary: 42B20

Rights: Copyright © 2006 Hokkaido University, Department of Mathematics

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Vol.35 • No. 3 • August 2006
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