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dc.contributor.authorSaber, Sayed ( Orcid Icon 0000-0002-5790-3222 )
dc.date.accessioned2022-02-09T17:16:27Z
dc.date.available2022-02-09T17:16:27Z
dc.date.issued2018-05-10
dc.identifier.citationSaber, S. (2018). Compactness of commutators of Toeplitz operators on q-pseudoconvex domains. Electronic Journal of Differential Equations, 2018(111), pp. 1-17.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15302
dc.description.abstractLet 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.formatText
dc.format.extent17 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subject∂ˉen_US
dc.subject∂ˉ-Neumann operatoren_US
dc.subjectBergman-Toeplitz operatoren_US
dc.subjectq-convex domainsen_US
dc.titleCompactness of commutators of Toeplitz operators on q-pseudoconvex domainsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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