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Keywords = generalized Campanato spaces

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14 pages, 309 KB  
Article
On the Commutators of Marcinkiewicz Integral with a Function in Generalized Campanato Spaces on Generalized Morrey Spaces
by Fuli Ku and Huoxiong Wu
Mathematics 2022, 10(11), 1817; https://doi.org/10.3390/math10111817 - 25 May 2022
Cited by 3 | Viewed by 2752
Abstract
This paper is devoted to exploring the mapping properties for the commutator μΩ,b generated by Marcinkiewicz integral μΩ with a locally integrable function b in the generalized Campanato spaces on the generalized Morrey spaces. Under the assumption that the [...] Read more.
This paper is devoted to exploring the mapping properties for the commutator μΩ,b generated by Marcinkiewicz integral μΩ 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 μΩ,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 BMO(Rn) and the Lipschitz spaces Lipα(Rn) (0<α1) as special examples. Some previous results are essentially improved and generalized. Full article
(This article belongs to the Special Issue Recent Advances in Harmonic Analysis and Applications)
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