Bulletin of the
Korean Mathematical Society BKMS

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: Primary 46E35, 42B25, 42B35

Supported by: This work was financially supported by Anhui Provincial Natural Science Foundation 1908085MA19 and Pre-research Project of the NNSF of China 2019yyzr14