Extrapolation in the scale of generalized reverse H\"older weights

TL;DR

This paper develops a new extrapolation theory for weights satisfying generalized reverse H"older inequalities within Orlicz spaces, extending prior work and enabling proofs of weighted norm inequalities for various operators.

Contribution

It introduces a generalized extrapolation framework in Orlicz spaces that broadens the scope of previous reverse H"older weight results.

Findings

Extended extrapolation results to Orlicz spaces.

Proved weighted norm inequalities for linear operators.

Applied the theory to bilinear operators.

Abstract

We develop a theory of extrapolation for weights that satisfy a generalized reverse H\"older inequality in the scale of Orlicz spaces. This extends previous results by Auscher and Martell [2] on limited range extrapolation. As an application, we show that a number of weighted norm inequalities for linear and bilinear operators can be proved using our extrapolation theorem.