Integral Operators on Generalized Weighted Central Morrey Spaces over Local Fields

TL;DR

This paper introduces generalized weighted central Morrey spaces over local fields and establishes boundedness estimates for Hardy--Hilbert-type and Hardy--Littlewood--Pólya operators within these spaces, focusing on power-weighted cases.

Contribution

It defines new function spaces over local fields and provides boundedness results for classical integral operators in these spaces, extending previous analysis to a broader setting.

Findings

Boundedness of Hardy--Hilbert-type operator on generalized weighted central Morrey spaces.

Boundedness of Hardy--Littlewood--Pólya operator on these spaces.

Results are specific to power-weighted cases.

Abstract

We introduce generalised weighted central Morrey spaces over local fields and obtain a quantitative estimate for the boundedness of the Hardy--Hilbert-type integral operator on these newly introduced spaces, albeit specifically in the context of power-weighted spaces. A similar estimate is also obtained for the Hardy--Littlewood--P\'olya operator.