Interpolation between Banach spaces and continuity of Radon-like integral transforms

TL;DR

This paper develops an abstract interpolation framework and applies it to analyze the continuity of Radon-like transforms, focusing on interpolation between H^1 and L^p spaces for analytic operator families.

Contribution

It introduces a new interpolation result between H^1 and L^p spaces for analytic operators, expanding the understanding of Radon-like transform continuity.

Findings

Established interpolation between H^1 and L^p spaces for analytic operators.

Demonstrated applications to Radon-like integral transforms.

Provided a unified framework for interpolation theory with new estimates.

Abstract

We present the abstract framework and some applications of interpolation theory. The main new result concerns interpolation between H^1 and L^p estimates for analytic families of operators acting on Schwartz functions.