Necessary and Sufficient Conditions for Boundedness of Commutators of Bilinear Fractional Integral Operators on Morrey Spaces |
Received:April 15, 2016 Revised:July 29, 2016 |
Key Words:
fractional integral operator Morrey spaces commutators ${\rm BMO}$ Lipschitz
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Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11261055; 11661075). |
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Abstract: |
In this paper, we obtain that $b\in {\rm BMO}(\mathbb{R}^n)$ if and only if the commutator $[b,I_{\alpha}]$ is bounded from the Morrey spaces $L^{p_1,\lambda_1}(\mathbb{R}^n)\times L^{p_2,\lambda_2}(\mathbb{R}^n)$ to $L^{q,\lambda}(\mathbb{R}^n)$, for some appropriate indices $p,q,\lambda,\mu$. Also we show that $b\in {\rm Lip}_{\beta}(\mathbb{R}^{n})$ if and only if the commutator $[b,I_{\alpha}]$ is bounded from the Morrey spaces $L^{p_1,\lambda_1}(\mathbb{R}^n)\times L^{p_2,\lambda_2}(\mathbb{R}^n)$ to $L^{q,\lambda}(\mathbb{R}^n)$, for some appropriate indices $p,q,\lambda,\mu$. |
Citation: |
DOI:10.3770/j.issn:2095-2651.2016.06.010 |
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