# A weighted transplantation theorem for Jacobi coefficients

## TL;DR

This paper proves a weighted transplantation theorem for Jacobi coefficients using a discrete Calderón-Zygmund approach, establishing boundedness and weak (1,1) estimates in weighted discrete spaces.

## Contribution

It introduces a new transplantation theorem for Jacobi coefficients in weighted spaces utilizing recent discrete vector-valued Calderón-Zygmund theory.

## Key findings

- Boundedness of transplantation operators on weighted ll^p spaces.
- Weighted weak (1,1) estimates for these operators.
- Extension of Calderón-Zygmund theory to discrete Jacobi coefficient settings.

## 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.