Discrete Rubio De Francia Extrapolation Theorems]{Discrete Rubio De Francia Extrapolation Theorems in The Theory of $\mathcal{B}_{p}-$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 $%
\mathcal{B}_{p}$-weights. We also present some extensions to the discrete $% B_{\infty }$-weights. The proof of the results based on the boundedness of
the discrete Hardy's operator and the self-improving property of the
discrete $\mathcal{B}_{p}$ weights. To the best of the authors' knowledge
the\ discrete extrapolation theorems in connection with $\mathcal{B}_{p}-$%
weights are essentially new$.$