Compact Bergman type operators

DOI10.1007/S11785-023-01419-8OpenAlexW4389086655MaRDI QIDQ6186078

Lijia Ding

Publication date: 9 January 2024

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-023-01419-8

zbMATH Keywords

dimensionBergman kernelcompact operatorDixmier traceSchatten classMacaev class

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Linear operators defined by compactness properties (47B07) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Cites Work

• Dixmier trace for Toeplitz operators on symmetric domains
• \(L^p\)-\(L^q\) estimates for Bergman projections in bounded symmetric domains of tube type
• Interpolation of compactness using Aronszajn-Gagliardo functors
• Characterization of the unit ball in \(\mathbb{C}^n\) by its automorphism group
• Estimates for the Bergman and Szegö projections on strongly pseudo-convex domains
• The singular integral operator induced by Drury-Arveson kernel
• Schatten class Bergman-type and Szegö-type operators on bounded symmetric domains
• The \(L^p\)-\(L^q\) boundedness and compactness of Bergman type operators
• Singular integral operators with Bergman-Besov kernels on the ball
• Toeplitz operators on Arveson and Dirichlet spaces
• A remark on Schatten class Toeplitz operators on Bergman spaces
• Spaces of Holomorphic Functions in the Unit Ball
• Estimates for the Bergman and Szegö projections in two symmetric domains of $ℂ^{n}$
• The hyper-singular cousin of the Bergman projection
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