Rubio de Francia Extrapolation Theorem for Quasi non-increasing Sequences

TL;DR

This paper extends the Rubio de Francia extrapolation theorem to quasi non-increasing sequences with specific weight classes and characterizes the boundedness of a generalized Hardy averaging operator in this context.

Contribution

It introduces a discrete extrapolation theorem for quasi non-increasing sequences and provides a weight characterization for the boundedness of a generalized Hardy operator.

Findings

Proved the Rubio de Francia extrapolation theorem for quasi non-increasing sequences.

Characterized the weights for boundedness of the generalized Hardy averaging operator.

Extended classical results to a new class of sequences and weights.

Abstract

We prove the discrete Rubio de Francia extrapolation theorem for a pair of quasi non-increasing sequences with $\mathcal{QB}_{\beta, p}$ weight class. Also, a weight characterization of the boundedness of the generalized discrete Hardy averagin19g operator on the class of quasi non-increasing sequences from $l_w^p(\mathbb{Z}^+)$ is proved.