Discrete Rubio De Francia extrapolation theorems in the theory of Bp−discrete weights

Abstract

In this paper, we will prove some discrete Rubio De Francia extrapolation theorems for nonincreasing sequences in the setting of the discrete Bp-weights. We also present some extensions to the discrete B?-weights. The proof of the results based on the boundedness of the discrete Hardy operator and the self-improving property of the discrete Bp weights. To the best of the authors? knowledge the discrete extrapolation theorems in connection with Bp?weights are essentially new.