Boundedness of the fractional maximal operator on variable exponent Lebesgue spaces: a short proof

TL;DR

This paper presents a simplified proof demonstrating the boundedness of the fractional maximal operator on variable exponent Lebesgue spaces, offering an alternative to previous complex proofs.

Contribution

It introduces a straightforward proof technique for the boundedness of the fractional maximal operator on variable exponent Lebesgue spaces, simplifying existing methods.

Findings

Simplified proof of boundedness

Alternative approach to previous proofs

Enhanced understanding of operator behavior

Abstract

We give a simple proof of the boundedness of the fractional maximal operator providing in this way an alternative approach to the one given by C. Capone, D. Cruz Uribe and A. Fiorenza in \cite{CCUF}.