Volume 55, Issue 2
Boundedness of Bilinear Fractional Integral Operators on Vanishing Generalized Morrey Spaces

J. Math. Study, 55 (2022), pp. 109-123.

Published online: 2022-04

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• Abstract

In this paper, we establish the boundedness of the bilinear fractional integral operator $B_\alpha$ and the subbilinear fractional maximal operator $M_\alpha$ on vanishing generalized Morrey spaces $V_{0}L^{p,\varphi}(\mathbb{R}^n)$, $V_{\infty}L^{p,\varphi}(\mathbb{R}^n)$ and $V^{(*)}L^{p,\varphi}(\mathbb{R}^n)$. The main novelty of this article is that we control $B_{\alpha}$ by the subbilinear maximal operator $M$ and $M_{\alpha'}$ with $\alpha'>\alpha$. Some specific examples for the main results of this paper are also included.

• Keywords

Bilinear fractional integral operator, subbilinear fractional maximal operator, generalized Morrey space, vanishing property.

26A33, 42B35, 42B25, 42B20

861733319@qq.com (Yuqin Liu)

xingfu@hubu.edu.cn (Xing Fu)

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@Article{JMS-55-109, author = {Yuqin and Liu and 861733319@qq.com and 23069 and Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China and Yuqin Liu and Xing and Fu and xingfu@hubu.edu.cn and 23070 and Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China and Xing Fu}, title = {Boundedness of Bilinear Fractional Integral Operators on Vanishing Generalized Morrey Spaces}, journal = {Journal of Mathematical Study}, year = {2022}, volume = {55}, number = {2}, pages = {109--123}, abstract = {

In this paper, we establish the boundedness of the bilinear fractional integral operator $B_\alpha$ and the subbilinear fractional maximal operator $M_\alpha$ on vanishing generalized Morrey spaces $V_{0}L^{p,\varphi}(\mathbb{R}^n)$, $V_{\infty}L^{p,\varphi}(\mathbb{R}^n)$ and $V^{(*)}L^{p,\varphi}(\mathbb{R}^n)$. The main novelty of this article is that we control $B_{\alpha}$ by the subbilinear maximal operator $M$ and $M_{\alpha'}$ with $\alpha'>\alpha$. Some specific examples for the main results of this paper are also included.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v55n2.22.01}, url = {http://global-sci.org/intro/article_detail/jms/20490.html} }
TY - JOUR T1 - Boundedness of Bilinear Fractional Integral Operators on Vanishing Generalized Morrey Spaces AU - Liu , Yuqin AU - Fu , Xing JO - Journal of Mathematical Study VL - 2 SP - 109 EP - 123 PY - 2022 DA - 2022/04 SN - 55 DO - http://doi.org/10.4208/jms.v55n2.22.01 UR - https://global-sci.org/intro/article_detail/jms/20490.html KW - Bilinear fractional integral operator, subbilinear fractional maximal operator, generalized Morrey space, vanishing property. AB -

In this paper, we establish the boundedness of the bilinear fractional integral operator $B_\alpha$ and the subbilinear fractional maximal operator $M_\alpha$ on vanishing generalized Morrey spaces $V_{0}L^{p,\varphi}(\mathbb{R}^n)$, $V_{\infty}L^{p,\varphi}(\mathbb{R}^n)$ and $V^{(*)}L^{p,\varphi}(\mathbb{R}^n)$. The main novelty of this article is that we control $B_{\alpha}$ by the subbilinear maximal operator $M$ and $M_{\alpha'}$ with $\alpha'>\alpha$. Some specific examples for the main results of this paper are also included.

Yuqin Liu & Xing Fu. (2022). Boundedness of Bilinear Fractional Integral Operators on Vanishing Generalized Morrey Spaces. Journal of Mathematical Study. 55 (2). 109-123. doi:10.4208/jms.v55n2.22.01
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