Uniform weighted inequalities for the Hankel transform transplantation operator

TL;DR

This paper establishes uniform weighted inequalities for the Hankel transform transplantation operator, including vector-valued inequalities, and extends a transference theorem, advancing the theoretical understanding of harmonic analysis tools.

Contribution

It introduces new uniform weighted inequalities for the Hankel transform transplantation operator and extends Rubio de Francia's transference theorem.

Findings

Established uniform weighted inequalities for the Hankel transform transplantation operator.

Derived a weighted vector-valued inequality.

Extended Rubio de Francia's transference theorem.

Abstract

In this paper we present uniform weighted inequalities for the Hankel transform transplantation operator. A weighted vector-valued inequality is also obtained. As a consequence we deduce an extension of a transference theorem due to Rubio de Francia.