Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1-15 |
| Seitenumfang | 15 |
| Fachzeitschrift | Integral Equations and Operator Theory |
| Jahrgang | 52 |
| Ausgabenummer | 1 |
| Publikationsstatus | Veröffentlicht - Mai 2005 |
| Extern publiziert | Ja |
Abstract
For the Segal-Bargmann space of Gaussian square integrable entire functions on ℂm we consider Hankel operators H f with symbols in f ∈ τ(ℂm). We completely characterize the functions in τ(ℂm) for which the operators H f and H̄f are simultaneously bounded or compact in terms of the mean oscillation of f. The analogous description holds for the commutators [M f , P] where M f denotes the "multiplication by f" and P is the Toeplitz projection. These results are already known in case of bounded symmetric domains Ω in ℂ m (see [BBCZ] or [C]). In the present paper we combine some techniques of [BBCZ] and [BC1]. Finally, we characterize the entire function f ∈H(ℂ) ∩ τ(ℂm) and the polynomials p in z and z̄ for which the Hankel operators Hf̄ and Hp are bounded (resp. compact).
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Algebra und Zahlentheorie
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in: Integral Equations and Operator Theory, Jahrgang 52, Nr. 1, 05.2005, S. 1-15.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Mean Oscillation and Hankel Operators on the Segal-Bargmann Space
AU - Bauer, Wolfram
N1 - Copyright: Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2005/5
Y1 - 2005/5
N2 - For the Segal-Bargmann space of Gaussian square integrable entire functions on ℂm we consider Hankel operators H f with symbols in f ∈ τ(ℂm). We completely characterize the functions in τ(ℂm) for which the operators H f and H̄f are simultaneously bounded or compact in terms of the mean oscillation of f. The analogous description holds for the commutators [M f , P] where M f denotes the "multiplication by f" and P is the Toeplitz projection. These results are already known in case of bounded symmetric domains Ω in ℂ m (see [BBCZ] or [C]). In the present paper we combine some techniques of [BBCZ] and [BC1]. Finally, we characterize the entire function f ∈H(ℂ) ∩ τ(ℂm) and the polynomials p in z and z̄ for which the Hankel operators Hf̄ and Hp are bounded (resp. compact).
AB - For the Segal-Bargmann space of Gaussian square integrable entire functions on ℂm we consider Hankel operators H f with symbols in f ∈ τ(ℂm). We completely characterize the functions in τ(ℂm) for which the operators H f and H̄f are simultaneously bounded or compact in terms of the mean oscillation of f. The analogous description holds for the commutators [M f , P] where M f denotes the "multiplication by f" and P is the Toeplitz projection. These results are already known in case of bounded symmetric domains Ω in ℂ m (see [BBCZ] or [C]). In the present paper we combine some techniques of [BBCZ] and [BC1]. Finally, we characterize the entire function f ∈H(ℂ) ∩ τ(ℂm) and the polynomials p in z and z̄ for which the Hankel operators Hf̄ and Hp are bounded (resp. compact).
KW - Hankel operators
KW - Mean oscillation
KW - Segal-Bargmann space
UR - http://www.scopus.com/inward/record.url?scp=21244493144&partnerID=8YFLogxK
U2 - 10.1007/s00020-003-1272-6
DO - 10.1007/s00020-003-1272-6
M3 - Article
AN - SCOPUS:21244493144
VL - 52
SP - 1
EP - 15
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 1
ER -