arXiv subjects

L. D. Edholm

Publications and source records attributed to L. D. Edholm.

5 recordsLinked to original sources

arXiv2020

The Leray transform: factorization, dual $CR$ structures and model hypersurfaces in $\mathbb{C}\mathbb{P}^2$

We compute the exact norms of the Leray transforms for a family $\mathcal{S}_β$ of unbounded hypersurfaces in two complex dimensions. The $\mathcal{S}_β$ generalize the Heisenberg group, and provide local projective approximations to any smooth, strongly $\mathbb{C}$-convex hypersurface $\mathcal{S}_β$ to two orders of tangency. This work is then examined in the context of projective dual $CR$-structures and the corresponding pair of canonical dual Hardy spaces associated to $\mathcal{S}_β$, leading to a universal description of the Leray transform and a factorization of the transform through orthogonal projection onto the conjugate dual Hardy space.

math.CV↗

arXiv2019

Sobolev mapping of some holomorphic projections

Sobolev irregularity of the Bergman projection on a family of domains containing the Hartogs triangle is shown. On the Hartogs triangle itself, a sub-Bergman projection is shown to satisfy better Sobolev norm estimates than its Bergman projection.

math.CV↗

arXiv2018

Duality and approximation of Bergman spaces

Expected duality and approximation properties are shown to fail on Bergman spaces of domains in $\mathbb{C}^n$, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation results are proved. Such operators are constructed on generalized Hartogs triangles. On a general bounded Reinhardt domain, norm convergence of Laurent series of Bergman functions is shown. This extends a classical result on Hardy spaces of the unit disc.

math.CV↗

arXiv2017

Bergman subspaces and subkernels: Degenerate $L^p$ mapping and zeroes

Regularity and irregularity of the Bergman projection on $L^p$ spaces is established on a natural family of bounded, pseudoconvex domains. The family is parameterized by a real variable $γ$. A surprising consequence of the analysis is that, whenever $γ$ is irrational, the Bergman projection is bounded only for $p=2$.

math.CV↗

arXiv2016

The Bergman projection on fat Hartogs triangles: L^p boundedness

A class of pseudoconvex domains in $\mathbb{C}^{n}$ generalizing the Hartogs triangle is considered. The $L^p$ boundedness of the Bergman projection associated to these domains is established, for a restricted range of $p$ depending on the "fatness" of domains. This range of $p$ is shown to be sharp.

math.CV↗