On the Commutators of Marcinkiewicz Integral with a Function in Generalized Campanato Spaces on Generalized Morrey Spaces

Fuli Ku and Huoxiong Wu
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Fuli Ku: School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
Huoxiong Wu: School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Mathematics, 2022, vol. 10, issue 11, 1-14

Abstract: This paper is devoted to exploring the mapping properties for the commutator μ Ω , b generated by Marcinkiewicz integral μ Ω with a locally integrable function b in the generalized Campanato spaces on the generalized Morrey spaces. Under the assumption that the integral kernel Ω satisfies certain log-type regularity, it is shown that μ Ω , b is bounded on the generalized Morrey spaces with variable growth condition, provided that b is a function in generalized Campanato spaces, which contain the B M O ( R n ) and the Lipschitz spaces Lip α ( R n ) ( 0 < α ≤ 1 ) as special examples. Some previous results are essentially improved and generalized.

Keywords: Marcinkiewicz integrals; commutators; generalized Campanato spaces; generalized Morrey spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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