Year: 2024
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.