A note on the weighted q-Hardy-Littlewood-type maximal operator with respect to q-Volkenborn integral in the p-adic integer ring

TL;DR

This paper introduces a weighted q-Hardy-Littlewood maximal operator based on p-adic q-invariant distributions, exploring its properties within the p-adic integer ring, contributing to p-adic harmonic analysis.

Contribution

It defines a new weighted q-Hardy-Littlewood maximal operator in the p-adic setting and investigates its fundamental properties.

Findings

Defined the weighted q-Hardy-Littlewood-type maximal operator

Established key properties of the operator

Enhanced understanding of p-adic harmonic analysis

Abstract

The essential aim of this paper is to define weighted q-Hardy-littlewood-type maximal operator by means of p-adic q-invariant distribution on Zp. Moreover, we give some interesting properties concerning this type maximal operator.