Sobolev regularity of the Bergman projection on certain pseudoconvex domains
In this paper we study the Sobolev regularity of the Bergman projection B and the ∂¯-Neumann operator N on a certain pseudoconvex domain. We show that if Ω is a domain with Lipschitz boundary, which is relatively compact in an n-dimensional compact Kähler manifold and satisfies some “logδ-pseudoconv...
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| Format: | Article |
| Language: | English |
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Elsevier
2017-04-01
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| Series: | Transactions of A. Razmadze Mathematical Institute |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2346809216300071 |
| Summary: | In this paper we study the Sobolev regularity of the Bergman projection B and the ∂¯-Neumann operator N on a certain pseudoconvex domain. We show that if Ω is a domain with Lipschitz boundary, which is relatively compact in an n-dimensional compact Kähler manifold and satisfies some “logδ-pseudoconvexity” condition, the operators B, N and ∂¯∗N are regular in the Sobolev spaces Wr,sk(Ω,E) for forms with values in a holomorphic vector bundle E and for any k<η/2, 0<η<1, 0≤r≤n, 0≤s≤n−1. Keywords: ∂¯-Neumann operator, Bergman projection, Kähler manifold, Pseudoconvex domain |
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| ISSN: | 2346-8092 |