Some spectral properties of the canonical solution operator to \(\overline{\partial}\) on weighted Fock spaces

DOI10.1016/j.jmaa.2010.10.074zbMath1210.47055arXiv1007.1082OpenAlexW1581265923MaRDI QIDQ626180

Olivia Constantin, Joaquim Ortega-Cerdà

Publication date: 22 February 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.1082

zbMATH Keywords

Fock spaceSchatten classescanonical solution operator to \(\overline{\partial}\)

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Spectral operators, decomposable operators, well-bounded operators, etc. (47B40) Quasi-analytic and other classes of functions of one complex variable (30D60)

Related Items (11)

Intermediate Hankel operators on the Fock space ⋮ Schatten class Hankel operators on exponential Bergman spaces ⋮ Sampling measure on doubling Fock spaces ⋮ Bergman spaces with exponential weights ⋮ Dixmier classes on generalized Segal-Bargmann-Fock spaces ⋮ Big Hankel operators on vector-valued Fock spaces in \(\mathbb {C}^d\) ⋮ Carleson measures and Toeplitz operators on doubling Fock spaces ⋮ A class of reverse Carleson measures on doubling Fock spaces ⋮ Atomic decomposition and duality for a class of Fock spaces ⋮ Fredholm Toeplitz operators on doubling Fock spaces ⋮ Hankel operators on exponential Bergman spaces

Cites Work

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• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
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• Membership of Hankel Operators on the Ball in Unitary Ideals
• Interpolation zwischen den Klassen 𝔖_p von Operatoren in Hilberträumen

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