Weighted p-Adic Hardy Operators and Their Commutators on p-Adic Central Morrey Spaces

In this paper, we establish necessary and sufficient conditions for boundedness of weighted p-adic Hardy operators on p-adic Morrey spaces, p-adic central Morrey spaces and p-adic lambda-central BMO spaces, respectively, and obtain their sharp bounds. We also give the characterization of weight functions for which the commutators generated by weighted p-adic Hardy operators and lambda-central BMO functions are bounded on the p-adic central Morrey spaces. This result is different from that on Euclidean spaces due to the special structure of p-adic integers.