Holomorphic projection and duality for domains in complex projective space

TL;DR

This paper investigates the relationship between Hardy spaces on dual convex hypersurfaces in complex projective space, demonstrating that the pairing's efficiency is quantified by the Leray transform's norm.

Contribution

It introduces a novel analysis of the duality and projection properties of Hardy spaces in complex projective geometry, linking pairing efficiency to the Leray transform.

Findings

The pairing between Hardy spaces is effectively measured by the Leray transform's norm.

Dual strongly C-linearly convex hypersurfaces exhibit a quantifiable projection efficiency.

The work advances understanding of invariant function spaces in complex projective geometry.

Abstract

We show that the efficiency of a natural pairing between certain projectively invariant Hardy spaces on dual strongly C-linearly convex real hypersurfaces in complex projective space is measured by the norm of the corresponding Leray transform.