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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2017-04-01
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| Series: | Transactions of A. Razmadze Mathematical Institute |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2346809216300071 |
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doaj-f185285ec6794d4289a019fb87493efa2020-11-24T22:01:12ZengElsevierTransactions of A. Razmadze Mathematical Institute2346-80922017-04-01171190102Sobolev regularity of the Bergman projection on certain pseudoconvex domainsSayed Saber0Mathematics Department, Faculty of Science, Beni-Suef University, EgyptIn 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 domainhttp://www.sciencedirect.com/science/article/pii/S2346809216300071 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Sayed Saber |
| spellingShingle |
Sayed Saber Sobolev regularity of the Bergman projection on certain pseudoconvex domains Transactions of A. Razmadze Mathematical Institute |
| author_facet |
Sayed Saber |
| author_sort |
Sayed Saber |
| title |
Sobolev regularity of the Bergman projection on certain pseudoconvex domains |
| title_short |
Sobolev regularity of the Bergman projection on certain pseudoconvex domains |
| title_full |
Sobolev regularity of the Bergman projection on certain pseudoconvex domains |
| title_fullStr |
Sobolev regularity of the Bergman projection on certain pseudoconvex domains |
| title_full_unstemmed |
Sobolev regularity of the Bergman projection on certain pseudoconvex domains |
| title_sort |
sobolev regularity of the bergman projection on certain pseudoconvex domains |
| publisher |
Elsevier |
| series |
Transactions of A. Razmadze Mathematical Institute |
| issn |
2346-8092 |
| publishDate |
2017-04-01 |
| description |
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 |
| url |
http://www.sciencedirect.com/science/article/pii/S2346809216300071 |
| work_keys_str_mv |
AT sayedsaber sobolevregularityofthebergmanprojectiononcertainpseudoconvexdomains |
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1725841072347676672 |