Boundedness of Commutators for Multilinear Marcinkiewicz Integrals with Generalized Campanato Functions on Generalized Morrey Spaces
Year: 2023
Author: Fuli Ku
Journal of Mathematical Study, Vol. 56 (2023), Iss. 4 : pp. 411–437
Abstract
This paper is devoted to exploring the mapping properties for the commutator $\mu_{Ω,\vec{b}}$ generated by multilinear Marcinkiewicz integral operators $\mu_Ω$ with a locally integrable function $\vec{b}= (b_1,···,b_m)$ on the generalized Morrey spaces. $\mu_{Ω,\vec{b}}$ is bounded from $L^{(p_1 ,\varphi_1)} (\mathbb{R}^n )×···×L^{(p_m,\varphi_m)} (\mathbb{R}^n)$ to $L ^{(q,\varphi)} (\mathbb{R}^n),$ where $L^{(p_i ,\varphi_i )} (\mathbb{R}^n),$ $L^{(q,φ)} (\mathbb{R}^n)$ are generalized Morrey spaces with certain variable growth condition, that $b_j(j=1,···,m)$ is a function in generalized Campanato spaces, which contain the BMO$(\mathbb{R}^n)$ and the Lipschitz spaces ${\rm Lip}_α(\mathbb{R}^n) (0<α≤1)$ as special examples.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v56n4.23.07
Journal of Mathematical Study, Vol. 56 (2023), Iss. 4 : pp. 411–437
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Multilinear Marcinkiewicz integrals commutators generalized Campanato spaces generalized Morrey spaces.