Boundedness and norm of certain p-adic Hardy-Littlewood-P\'{o}lya-type operators

TL;DR

This paper investigates the boundedness and norms of specific p-adic Hardy-Littlewood-Pólya-type operators on weighted Lebesgue spaces, providing complete characterizations and sharp estimates that extend prior results.

Contribution

It introduces parameters to define p-adic Hardy-Littlewood-Pólya operators and fully characterizes their boundedness and norms on weighted Lebesgue spaces, extending previous work.

Findings

Complete characterization of L^q-L^r boundedness

Sharp norm estimates for special cases

Extension of existing theoretical results

Abstract

In this paper, by introducing some parameters, we define and study certain $p$-adic Hardy-Littlewood-P\'{o}lya-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.