The boundedness of Fractional Hardy-Littlewood maximal operator on variable lp(Z) spaces using Calderon-Zygmund decomposition

TL;DR

This paper establishes boundedness properties of fractional Hardy-Littlewood maximal operators on variable sequence spaces using Calderon-Zygmund decomposition, extending classical results to more general variable exponent contexts.

Contribution

It introduces new boundedness results for fractional maximal operators on variable lp(Z) spaces utilizing Calderon-Zygmund decomposition techniques.

Findings

Proved strong and weak type inequalities for the operators.

Extended classical maximal operator bounds to variable exponent spaces.

Applied Calderon-Zygmund decomposition in a novel sequence space setting.

Abstract

In this paper, we prove strong type, weak type inequalities of Hardy-Littlewood maximal operator and fractional Hardy-Littlewood maximal operator on variable sequence spaces lp(Z). This is achieved using Calderon-Zygmund decomposition for sequences, properties of modular functional and Log Holder continuity.