Compactness of commutators of Toeplitz operators on q-pseudoconvex domains
| dc.contributor.author | Saber, Sayed | |
| dc.date.accessioned | 2022-02-09T17:16:27Z | |
| dc.date.available | 2022-02-09T17:16:27Z | |
| dc.date.issued | 2018-05-10 | |
| dc.description.abstract | Let Ω be a bounded q-pseudoconvex domain in ℂn, n ≥ 2 and let 1 ≤ q ≤ n - 1. If Ω is smooth, we find sufficient conditions for the ∂ˉ-Neumann operator to be compact. If Ω is non-smooth and if q ≤ p ≤ n - 1, we show that compactness of the ∂ˉ-Neumann operator, Np+1, on square integrable (0, p + 1)-forms is equivalent to compactness of the commutators [Bp, z̅j], 1 ≤ j ≤ n, on square integrable ∂ˉ-closed (0, p)-forms, where Bp is the Bergman projection on (0, p)-forms. Moreover, we prove that compactness of the commutator of Bp with bounded functions percolates up in the ∂ˉ-complex on ∂ˉ-closed forms and square integrable holomorphic forms. Furthermore, we find a characterization of compactness of the canonical solution operator, Sp+1, of the ∂ˉ-equation restricted on (0, p + 1)-forms with homomorphic coefficients in terms of compactness of commutators [Tpzj*, Tpzj], 1 ≤ j ≤ n, on (0, p)-forms with holomorphic coefficients, where Tpzj is the Bergman-Toeplitz operator acting on (0, p)-forms with symbol zj. This extends to domains which are not necessarily pseudoconvex. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 17 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Saber, S. (2018). Compactness of commutators of Toeplitz operators on q-pseudoconvex domains. <i>Electronic Journal of Differential Equations, 2018</i>(111), pp. 1-17. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15302 | |
| 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, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | ∂ˉ | |
| dc.subject | ∂ˉ-Neumann operator | |
| dc.subject | Bergman-Toeplitz operator | |
| dc.subject | q-convex domains | |
| dc.title | Compactness of commutators of Toeplitz operators on q-pseudoconvex domains | |
| dc.type | Article |