Tent Space Boundedness Via Extrapolation

TL;DR

This paper investigates the boundedness of various operators on tent spaces using extrapolation techniques, extending results to non-Banach spaces and exploring implications for amalgam spaces.

Contribution

It introduces new boundedness results for operators on tent spaces via extrapolation and atomic theory, including non-Banach space cases.

Findings

Boundedness of maximal and Calderón-Zygmund operators on tent spaces

Extension of boundedness results to non-Banach spaces

Implications for amalgam spaces

Abstract

We study the action of operators on tent spaces such as maximal operators, Calder{\'o}n-Zygmund operators, Riesz potentials. We also consider singular non-integral operators. We obtain boundedness as an application of extrapolation methods in the Banach range. In the non Banach range, boundedness results for Calder{\'o}n-Zygmund operators follows by using an appropriate atomic theory. We end with some consequences on amalgalm spaces.