$p$-adic singular integral and their commutator in generalized Morrey space

Abstract

For a prime number $p,$ let ${\mathbb{Q}}_p$ be the field of $p$-adic numbers. In this paper, we established the boundedness of a class of $p$-adic singular integral operators on the $p$-adic generalized Morrey spaces. The corresponding boundedness for the commutators generalized by the $p$-adic singular integral operators and $p$-adic Lipschitz functions or $p$-adic generalized Campanato functions is also considered.