Compactness of the canonical solution operator on Lipschitz q-pseudoconvex boundaries
| dc.contributor.author | Saber, Sayed | |
| dc.date.accessioned | 2021-11-05T16:08:12Z | |
| dc.date.available | 2021-11-05T16:08:12Z | |
| dc.date.issued | 2019-04-10 | |
| dc.description.abstract | Let Ω ⊂ ℂn be a bounded Lipschitz q-pseudoconvex domain that admit good weight functions. We shall prove that the canonical solution operator for the the ∂¯-equation is compact on the boundary of Ω and is bounded in the Sobolev space Wkr,s(Ω) for some values of k. Moreover, we show that the Bergman projection and the ∂¯-Neumann operator are bounded in the Sobolev space Wkr,s(Ω) for some values of k. If Ω is smooth, we shall give sufficient conditions for compactness of the ∂¯-Neumann operator. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 22 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Saber, S. (2019). Compactness of the canonical solution operator on Lipschitz q-pseudoconvex boundaries. <i>Electronic Journal of Differential Equations, 2019</i>(48), pp. 1-22. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14781 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Lipschitz domain | |
| dc.subject | q-Pseudoconvex domain | |
| dc.title | Compactness of the canonical solution operator on Lipschitz q-pseudoconvex boundaries | en_US |
| dc.type | Article |