Rubio de Francia Extrapolation Theorems for Quasi-Monotone Functions

Abstract

We prove Rubio de Francia extrapolation results in Lebesgue and grand Lebesgue spaces for quasi monotone functions with QB β,p weights. The extrapolation in Lebesgue spaces with the weight class QB β,∞ 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.