Volume 32, Issue 2
Multilinear Fractional Integrals and Commutators on Generalized Herz Spaces

Anal. Theory Appl., 32 (2016), pp. 103-121.

Published online: 2016-04

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• Abstract

Suppose $\vec{b}=(b_1,\cdots,b_m)\in (BMO)^m,$ $I_{\alpha,m}^{{\Pi b}}$ is the iterated commutator of $\vec{b}$ and the $m$-linear multilinear fractional integral operator $I_{\alpha,m}$. The purpose of this paper is to discuss the boundedness properties of $I_{\alpha,m}$ and $I_{\alpha,m}^{{\Pi b}}$ on generalized Herz spaces with general Muckenhoupt weights.

• Keywords

Multilinear fractional integral, generalized Herz space, commutator, Muckenhoupt weight.

42B20, 42B35

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@Article{ATA-32-103, author = {}, title = {Multilinear Fractional Integrals and Commutators on Generalized Herz Spaces}, journal = {Analysis in Theory and Applications}, year = {2016}, volume = {32}, number = {2}, pages = {103--121}, abstract = {

Suppose $\vec{b}=(b_1,\cdots,b_m)\in (BMO)^m,$ $I_{\alpha,m}^{{\Pi b}}$ is the iterated commutator of $\vec{b}$ and the $m$-linear multilinear fractional integral operator $I_{\alpha,m}$. The purpose of this paper is to discuss the boundedness properties of $I_{\alpha,m}$ and $I_{\alpha,m}^{{\Pi b}}$ on generalized Herz spaces with general Muckenhoupt weights.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2016.v32.n2.1}, url = {http://global-sci.org/intro/article_detail/ata/4658.html} }
TY - JOUR T1 - Multilinear Fractional Integrals and Commutators on Generalized Herz Spaces JO - Analysis in Theory and Applications VL - 2 SP - 103 EP - 121 PY - 2016 DA - 2016/04 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n2.1 UR - https://global-sci.org/intro/article_detail/ata/4658.html KW - Multilinear fractional integral, generalized Herz space, commutator, Muckenhoupt weight. AB -

Suppose $\vec{b}=(b_1,\cdots,b_m)\in (BMO)^m,$ $I_{\alpha,m}^{{\Pi b}}$ is the iterated commutator of $\vec{b}$ and the $m$-linear multilinear fractional integral operator $I_{\alpha,m}$. The purpose of this paper is to discuss the boundedness properties of $I_{\alpha,m}$ and $I_{\alpha,m}^{{\Pi b}}$ on generalized Herz spaces with general Muckenhoupt weights.

Y. Wang & Y. He. (1970). Multilinear Fractional Integrals and Commutators on Generalized Herz Spaces. Analysis in Theory and Applications. 32 (2). 103-121. doi:10.4208/ata.2016.v32.n2.1
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