Boundedness and Compactness of Multilinear Singular Integrals on Morrey Spaces

Boundedness and Compactness of Multilinear Singular Integrals on Morrey Spaces

Year:    2024

Author:    Ting Mei, Aobo Li

Journal of Mathematical Study, Vol. 57 (2024), Iss. 2 : pp. 164–177

Abstract

In this paper, we consider the boundedness and compactness of the multilinear singular integral operator on Morrey spaces, which is defined by $$T_Af(x)={\rm p.v.}\int_{\mathbb{R}^n}\frac{\Omega(x-y)}{|x-y|^{n+1}}R(A;x,y)f(y)dy,$$ where $R(A;x,y)=A(x)−A(y)−∇A(y)·(x−y)$ with $D^βA∈BMO(\mathbb{R}^n)$ for all $|β|=1.$ We prove that $T_A$ is bounded and compact on Morrey spaces $L^{p,λ}(\mathbb{R}^n)$ for all $1<p<∞$ with $Ω$ and $A$ satisfying some conditions. Moreover, the boundedness and compactness of the maximal multilinear singular integral operator $T_{A,∗}$ on Morrey spaces are also given in this paper.


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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v57n2.24.03

Journal of Mathematical Study, Vol. 57 (2024), Iss. 2 : pp. 164–177

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Multilinear operator compactness rough kernel Morrey space.

Author Details

Ting Mei

Aobo Li