Rubio de Francia Extrapolation Theorems for Quasi-Monotone Functions

TL;DR

This paper extends Rubio de Francia extrapolation theorems to quasi-monotone functions with specific weight classes in Lebesgue and grand Lebesgue spaces, and characterizes the Hardy averaging operator's boundedness in these contexts.

Contribution

It introduces new extrapolation results for quasi-monotone functions with $QB_{eta,p}$ weights and explores their implications for Hardy operator boundedness.

Findings

Extrapolation results for quasi-monotone functions with $QB_{eta,p}$ weights.

Characterization of Hardy averaging operator boundedness in grand Lebesgue spaces.

Extension of extrapolation to $QB_{eta, ext{infty}}$ weight class.

Abstract

We prove Rubio de Francia extrapolation results in Lebesgue and grand Lebesgue spaces for quasi monotone functions with $QB_{\beta,p}$ weights. The extrapolation in Lebesgue spaces with the weight class $QB_{\beta,\infty}$ has also been investigated. As an application, we characterize the boundedness of the Hardy averaging operator for quasi monotone functions in the grand Lebesgue spaces.