p-adic singular integrals and their commutators in generalized Morrey spaces

Abstract

Abstract For a prime number p, let Qp $\mathbb{Q}_{p}$ be the field of p-adic numbers. In this paper, we establish the boundedness of a class of p-adic singular integral operators on the p-adic generalized Morrey spaces. We also consider 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.

Keywords

• p-adic field
• p-adic singular integral operator
• Commutator
• p-adic generalized Morrey function
• p-adic generalized Campanato function
• p-adic Lipschitz function