Multilinear Calder\'{o}n-Zygmund operators and their commutators on central Morrey spaces with variable exponent
Bull. Korean Math. Soc.
Published online July 15, 2020
Liwei Wang
Anhui Polytechnic University
Abstract : In this paper, we establish the boundedness of the $m$-linear Calder\'{o}n-Zygmund operators on product of central Morrey spaces with variable exponent. The corresponding boundedness properties of their commutators with $\lambda$-central {\rm BMO} symbols are also considered. Finally, we prove that the multilinear commutators of Calder\'{o}n-Zygmund singular integrals introduced by P\'{e}rez and Trujillo-Gonz\'{a}lez are bounded on central Morrey spaces with variable exponent. Our results improve and generalize some previous classical results to the variable exponent setting.
Keywords : Variable exponent; central Morrey spaces; $m$-linear Calder\'{o}n-Zygmund operators; multilinear commutator
MSC numbers : 46E35, 42B25, 42B35
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