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 $Q{B}_{\beta ,p}$ weights. The extrapolation in Lebesgue spaces with the weight class $Q{B}_{\beta ,\infty }$ 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.

13 pages