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HANKEL MEASURES FOR FOCK SPACE

Part of: Spaces and algebras of analytic functions Measures, integration, derivative, holomorphy

Published online by Cambridge University Press:  15 September 2022

ERMIN WANG Open the ORCID record for ERMIN WANG [Opens in a new window]
ERMIN WANG*
Affiliation:
School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, Guangdong 524048, PR China
*
e-mail: wem0913@sina.com
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Abstract

Inspired by Xiao’s work on Hankel measures for Hardy and Bergman spaces [‘Pseudo-Carleson measures for weighted Bergman spaces’. Michigan Math. J. 47 (2000), 447–452], we introduce Hankel measures for Fock space $F^p_\alpha $ . Given $p\ge 1$ , we obtain several equivalent descriptions for such measures on $F^p_\alpha $ .

Keywords

Fock spaceHankel measureCarleson measure

MSC classification

Primary: 30H20: Bergman spaces, Fock spaces
Secondary: 46G12: Measures and integration on abstract linear spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 2 , April 2023 , pp. 290 - 295
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The author is supported by NNSF of China (12001258) and Lingnan Normal University (ZL1925).

References

Arcozzi, N., Rochberg, R., Sawyer, E. and Wick, B., ‘Function spaces related to the Dirichlet space’, J. Lond. Math. Soc. (2) 83 (2011), 1–18.CrossRefGoogle Scholar
Bao, G., Ye, F. and Zhu, K., ‘Hankel measures for Hardy spaces’, J. Geom. Anal. 31 (2021), 5131–5145.CrossRefGoogle Scholar
Hu, Z. and Lv, X., ‘Toeplitz operators from one Fock space to another’, Integral Equations Operator Theory 70 (2011), 541–559.CrossRefGoogle Scholar
Janson, S., Peetre, J. and Rochberg, R., ‘Hankel forms and the Fock space’, Rev. Mat. Iberoam. 3 (1987), 61–138.CrossRefGoogle Scholar
Luecking, D., ‘Trace ideal criteria for Toeplitz operators’, J. Funct. Anal. 73 (1987), 345–368.CrossRefGoogle Scholar
Xiao, J., ‘Pseudo–Carleson measures for weighted Bergman spaces’, Michigan Math. J. 47 (2000), 447–452.CrossRefGoogle Scholar
Xiao, J., ‘Hankel measures on Hardy space’, Bull. Aust. Math. Soc. 62 (2000), 135–140.CrossRefGoogle Scholar
Zhu, K., Analysis on Fock Spaces (Springer, New York, 2012).CrossRefGoogle Scholar