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

Abstract Generalizing a result of Berndtsson and Charpentier, we provide sufficient conditions for $$L^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> Sobolev regularity of the Bergman projection acting on $$L^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> 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.