A note on Rubio de Francia's extrapolation in tent spaces and applications

TL;DR

This paper extends Rubio de Francia's extrapolation theorem to tent spaces, enabling the derivation of new weighted estimates for various operators, including Calderón-Zygmund and fractional operators, with broad applications in harmonic analysis.

Contribution

The paper generalizes the extrapolation principle to tent spaces, providing a new tool for obtaining weighted estimates for a wide class of operators.

Findings

Extended extrapolation to tent spaces.

Derived new weighted estimates for Calderón-Zygmund operators.

Reproved existing estimates using the new extrapolation method.

Abstract

The Rubio de Francia extrapolation theorem is a very powerful result which states that in order to show that certain operators satisfy weighted norm inequalities with Muckenhoupt weights it suffices to see that the corresponding inequalities hold for some fixed exponent, for instance $p=2$. In this paper we extend this result and show that this extrapolation principle allows one to obtain weighted estimates in tent spaces. From our extrapolation result we automatically derive new estimates (and reprove some other) concerning Calder\'on-Zygmund operators, operators associated with the Kato conjecture, or fractional operators.