BOUNDS FOR MULTILINEAR OPERATORS UNDER AN INTEGRAL TYPE CONDITION ON MORREY SPACES

Qianjun HE; Xinfeng WU; Dunyan YAN

doi:10.1007/s10473-022-0322-6

Acta mathematica scientia, Series B >

2022 , Vol. 42 >Issue 3: 1191 - 1208

DOI: https://doi.org/10.1007/s10473-022-0322-6

Articles

BOUNDS FOR MULTILINEAR OPERATORS UNDER AN INTEGRAL TYPE CONDITION ON MORREY SPACES

Qianjun HE ,
Xinfeng WU ,
Dunyan YAN

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1. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, China;
2. Department of Mathematics, China University Mining & Technology(Beijing), Beijing, 100083, China;
3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

Received date: 2020-12-24

Revised date: 2021-06-06

Online published: 2022-06-24

Supported by

This work was supported by National Natural Science Foundation of China (11871452, 12071473) and the Beijing Information Science and Technology University Foundation (2025031).

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Abstract

In this paper, we study a boundedness property of the Adams type for multilinear fractional integral operators with the multilinear $L^{r^{\prime},\alpha}$-Hörmander condition and their commutators with vector valued BMO functions on a Morrey space and a predual Morrey space. Moreover, we give an endpoint estimate for multilinear fractional integral operators. As an application, we obtain the boundedness of multilinear Fourier multipliers with limited Sobolev regularity on a Morrey space.

Key words： Multilinear fractional integral; $L^{r^{\prime},\alpha}$-Hörmander condition; commutators; BMO spaces; Morrey spaces; multilinear Fourier multiplier

Cite this article

Qianjun HE , Xinfeng WU , Dunyan YAN . BOUNDS FOR MULTILINEAR OPERATORS UNDER AN INTEGRAL TYPE CONDITION ON MORREY SPACES[J]. Acta mathematica scientia, Series B, 2022 , 42(3) : 1191 -1208 . DOI: 10.1007/s10473-022-0322-6

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