Projectively Invariant Hardy Spaces on Domains with Corners

Benjamin Krakoff

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arXiv · 2205.05761

Projectively Invariant Hardy Spaces on Domains with Corners

Benjamin Krakoff

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Abstract

For smoothly bounded, strongly $\mathbb{C}$-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 $\mathbb{C}$-convexity that is compatible with Cauchy-Fantappi\'e-Leray kernels, and thus define projectively invariant Hardy spaces as in the smooth case.

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Benjamin Krakoff. 2022-05-11. Projectively Invariant Hardy Spaces on Domains with Corners. https://arxiv.org/abs/2205.05761

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