Projectively Invariant Hardy Spaces on Domains with Corners

2022/05/11 by Benjamin Krakoff, Krakoff, Benjamin
Mathematics · #32F99 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:32F99

paper · pdf · doi:10.48550/arxiv.2205.05761

21 pages, 3 figures

arxiv created 2022/05/11 · openalex publication_date 2022/05/11 · arxiv updated 2022/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For smoothly bounded, strongly ℂ-convex domains, one can use the Fefferman form or its variants to define projectively invariant norms on sections of holomorphic line bundles, producing a Hardy space. In two variables, we construct a projectively invariant measure on the singular part of a piece-wise smooth domain, and show that positivity of this invariant coincides with a notion of strong ℂ-convexity that is compatible with Cauchy-Fantappié-Leray kernels, and thus define projectively invariant Hardy spaces as in the smooth case.

Related

• Holomorphic projection and duality for domains in complex projective space
• The Smoothness of kernel in Hardy spaces
• The Laplace and Leray transforms on some (weakly) convex domains in ℂ²
• Morse properties in convex projective geometry
• Hardy Spaces over Half-strip Domains