A duality for the double fibration transform

TL;DR

This paper introduces a duality in the spectral sequence of the holomorphic double fibration transform, enhancing understanding of its injectivity and range, with applications to Hermitian cases.

Contribution

It establishes a new duality within the spectral sequence framework for the double fibration transform, improving theoretical understanding and applications.

Findings

Duality in the spectral sequence for the transform

Results on injectivity and range characterization

Enhanced duality in Hermitian holomorphic cases

Abstract

We establish a duality within the spectral sequence that governs the holomorphic double fibration transform. It has immediate application to the questions of injectivity and range characterization for this transform. We discuss some key examples and an improved duality that holds in the Hermitian holomorphic case.