On the Commutators of Marcinkiewicz Integral with a Function in Generalized Campanato Spaces on Generalized Morrey Spaces - Fuli Ku; Huoxiong Wu (Mathematics, 2022)
This paper is devoted to exploring the mapping properties for the commutator <semantics>μΩ,b</semantics> generated by Marcinkiewicz integral <semantics>μΩ</semantics> with a locally integrable function b in the generalized Campanato spaces on the generalized Morrey spaces. Under the assumption that the integral kernel <semantics>Ω</semantics> satisfies certain log-type regularity, it is shown that <semantics>μΩ,b</semantics> is bounded on the generalized Morrey spaces with variable growth condition, provided that b is a function in generalized Campanato spaces, which contain the <semantics>BMO(Rn)</semantics> and the Lipschitz spaces <semantics>Lipα(Rn)</semantics> (<semantics>0<α≤1</semantics>) as special examples. Some previous results are essentially improved and generalized.