Theory of discrete Muckenhoupt weights and discrete Rubio de Francia extrapolation theorems

Abstract

In this paper, we will prove a discrete Rubio De Francia extrapolation theorem in the theory of discrete Ap-Muckenhoupt weights for which the discrete Hardy-Littlewood maximal operator is bounded on lpw (Z+). The results will be proved by employing the self-improving property of the discrete Ap-Muckenhoupt weights and the Marcinkiewicz Interpolation Theorem.