Abstract
We establish the Hardy-Littlewood-Sobolev inequalities onp-adic central Morrey spaces. Furthermore, we obtain theλ-central BMO estimates for commutators ofp-adic Riesz potential onp-adic central Morrey spaces.
Highlights
IntroductionThe Riesz potential operator Iα for all locally integrable functions f on is defined Rn, by
This paper focuses on the Riesz potentials on p-adic field
For a prime number p, the field of p-adic numbers Qp is defined as the completion of the field of rational numbers Q with respect to the non-Archimedean p-adic norm | ⋅ |p, which satisfies |x|p = 0 if and only if x = 0; |xy|p = |x|p|y|p; |x + y|p ≤ max{|x|p, |y|p}
Summary
The Riesz potential operator Iα for all locally integrable functions f on is defined Rn, by. It is well-known that Qnp is a classical kind of locally compact Vilenkin groups. Like on Euclidean spaces, using the Riesz potential with n > 2 and α = 2, one can introduce the p-adic Laplacians [13]. We will consider the Riesz potentials and their commutators with p-adic central BMO functions on padic central Morrey spaces. The p-adic central Morrey space Ḃq,λ(Qnp) is defined by. The p-adic weak central Morrey space WḂq,λ(Qnp) is defined by. Throughout this paper the letter C will be used to denote various constants, and the various uses of the letter do not, denote the same constant
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