A weighted transplantation theorem for Jacobi coefficients

Abstract

We present a transplantation theorem for Jacobi coefficients in weighted spaces. In fact, by using a discrete vector-valued local Calder\'{o}n-Zygmund theory, which has recently been furnished, we prove the boundedness of transplantation operators from $\ell^p(\mathbb{N},w)$ into itself, where $w$ is a weight in the discrete Muckenhoupt class $A_{p}(\mathbb{N})$. Moreover, we obtain weighted weak $(1,1)$ estimates for those operators.