Boundedness and norm of certain p-adic Hardy-Littlewood-Pólya-type operators

Abstract

In this paper, by introducing some parameters, we define and study certain $p$-adic Hardy-Littlewood-Pólya-type integral operators acting on $p$-adic weighted Lebesgue spaces. We completely characterize $L^q-L^r$ boundedness of these operators for all $(q,r)\in [1,\infty ]\times [1,\infty ]$. For some special cases, we obtain sharp norm estimates for the operators. These results are not only a complement to some previous results but also an extension of existing ones in the literature.

22 pages