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 Calderón–Zygmund theory, which has recently been furnished, we prove the boundedness of transplantation operators from ℓp(N,w) into itself, where w is a weight in the discrete Muckenhoupt class Ap(N). Moreover, we obtain weighted weak (1,1) estimates for those operators.