English

Sobolev Regularity for the Bergman Projection on Relatively Compact Domains in Hermitian manifolds

Complex Variables 2024-10-17 v1

Abstract

Generalizing a result of Berndtsson and Charpentier, we provide sufficient conditions for L2L^2 Sobolev regularity of the Bergman projection acting on L2L^2 sections of a holomorphic line bundle restricted to a relatively compact domain with Lipschitz boundary in a Hermitian manifold. We provide examples to show that our methods work for domains in Hopf manifolds endowed with a suitable Hermitian metric.

Keywords

Cite

@article{arxiv.2410.12715,
  title  = {Sobolev Regularity for the Bergman Projection on Relatively Compact Domains in Hermitian manifolds},
  author = {Phillip S. Harrington},
  journal= {arXiv preprint arXiv:2410.12715},
  year   = {2024}
}