Details
| Original language | English |
|---|---|
| Pages (from-to) | 293-319 |
| Number of pages | 27 |
| Journal | Tokyo journal of mathematics |
| Volume | 31 |
| Issue number | 2 |
| Publication status | Published - 1 Dec 2008 |
| Externally published | Yes |
Abstract
Let H be a reproducing kernel Hilbert space contained in a wider space L2(X, μ). We study the Hilbert-Schmidt property of Hankel operators Hg on H with bounded symbol g by analyzing the behavior of the iterated Berezin transform. We determine symbol classes S such that for g ∈ S the Hilbert-Schmidt property of Hg implies that Hḡ is a Hilbert-Schmidt operator as well and there is a norm estimate of the form ‖Hḡ‖HS ≤ C ‖ Hg ‖ HS. Finally, applications to the case of Bergman spaces over strictly pseudo convex domains in Cn, the Fock space, the pluri-harmonic Fock space and spaces of holomorphic functions on a quadric are given.
Keywords
- Berezin transform, Complex projective space, Hilbert-Schmidt Hankel operators, Kernel asymptotic, Pairing of polarizations, Reproducing kernel, Sphere
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Tokyo journal of mathematics, Vol. 31, No. 2, 01.12.2008, p. 293-319.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Hilbert-Schmidt Hankel Operators and Berezin Iteration
AU - Bauer, Wolfram
AU - Furutani, Kenro
N1 - Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2008/12/1
Y1 - 2008/12/1
N2 - Let H be a reproducing kernel Hilbert space contained in a wider space L2(X, μ). We study the Hilbert-Schmidt property of Hankel operators Hg on H with bounded symbol g by analyzing the behavior of the iterated Berezin transform. We determine symbol classes S such that for g ∈ S the Hilbert-Schmidt property of Hg implies that Hḡ is a Hilbert-Schmidt operator as well and there is a norm estimate of the form ‖Hḡ‖HS ≤ C ‖ Hg ‖ HS. Finally, applications to the case of Bergman spaces over strictly pseudo convex domains in Cn, the Fock space, the pluri-harmonic Fock space and spaces of holomorphic functions on a quadric are given.
AB - Let H be a reproducing kernel Hilbert space contained in a wider space L2(X, μ). We study the Hilbert-Schmidt property of Hankel operators Hg on H with bounded symbol g by analyzing the behavior of the iterated Berezin transform. We determine symbol classes S such that for g ∈ S the Hilbert-Schmidt property of Hg implies that Hḡ is a Hilbert-Schmidt operator as well and there is a norm estimate of the form ‖Hḡ‖HS ≤ C ‖ Hg ‖ HS. Finally, applications to the case of Bergman spaces over strictly pseudo convex domains in Cn, the Fock space, the pluri-harmonic Fock space and spaces of holomorphic functions on a quadric are given.
KW - Berezin transform
KW - Complex projective space
KW - Hilbert-Schmidt Hankel operators
KW - Kernel asymptotic
KW - Pairing of polarizations
KW - Reproducing kernel
KW - Sphere
UR - http://www.scopus.com/inward/record.url?scp=77951937318&partnerID=8YFLogxK
U2 - 10.3836/tjm/1233844053
DO - 10.3836/tjm/1233844053
M3 - Article
AN - SCOPUS:77951937318
VL - 31
SP - 293
EP - 319
JO - Tokyo journal of mathematics
JF - Tokyo journal of mathematics
SN - 0387-3870
IS - 2
ER -