全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

加权Fock空间上乘法算子的有界性和紧性
The Boundedness and Compactness of Multiplication Operators on Weighted Fock Spaces

DOI: 10.12677/pm.2025.151005, PP. 40-46

Keywords: 加权Fock空间,乘法算子,有界性,紧性
Weighted Fock Spaces
, Multiplication Operator, Boundedness, Compactness

Full-Text   Cite this paper   Add to My Lib

Abstract:

本文凭借逐点估计、范数估计等相关技巧,给出了指标不同的加权Fock空间中乘法算子有界性与紧性的等价描述。
In this paper, by pointwise estimation, norm estimation and other related techniques, the equivalent descriptions of the boundedness and compactness of multiplication operators in weighted Fock spaces with different indices are presented.

References

[1]  Baker, I.N., Deddens, J.A. and Ullman, J.L. (1974) A Theorem on Entire Functions with Applications to Toeplitz Operators. Duke Mathematical Journal, 41, 739-745.
https://doi.org/10.1215/s0012-7094-74-04177-5
[2]  Abrahamse, M.B. and Douglas, R.G. (1976) A Class of Subnormal Operators Related to Multiply-Connected Domains. Advances in Mathematics, 19, 106-148.
https://doi.org/10.1016/0001-8708(76)90023-2
[3]  Cowen, C. (1980) The Commutant of an Analytic Toeplitz Operator, II. Indiana University Mathematics Journal, 29, 1-12.
https://doi.org/10.1512/iumj.1980.29.29001
[4]  Zhu, K. (2000) Reducing Subspaces for a Class of Multiplication Operators. Journal of the London Mathematical Society, 62, 553-568.
https://doi.org/10.1112/s0024610700001198
[5]  Zhang, K., Feng, X. and Dong, J.G. (2015) Multiplication Operator on the Weighted Bergman Space of the Unit Ball. Acta Mathematica Sinica, 58, 125-130.
[6]  Girela, D. and Peláez, J.Á. (2006) Carleson Measures, Multipliers and Integration Operators for Spaces of Dirichlet Type. Journal of Functional Analysis, 241, 334-358.
https://doi.org/10.1016/j.jfa.2006.04.025
[7]  Galanopoulos, P., Girela, D. and Peláez, J.Á. (2011) Multipliers and Integration Operators on Dirichlet Spaces. Transactions of the American Mathematical Society, 363, 1855-1855.
https://doi.org/10.1090/s0002-9947-2010-05137-2
[8]  Zhu, K.H. (2012) Analysis on Fock Spaces. Springer.
[9]  Isralowitz, J. (2014) Invertible Toeplitz Products, Weighted Norm Inequalities, and Ap Weights. Journal of Operator Theory, 71, 381-410.
https://doi.org/10.7900/jot.2012apr10.1989
[10]  Cascante, C., Fàbrega, J. and Peláez, J.A. (2018) Littlewood-Paley Formulas and Carleson Measures for Weighted Fock Spaces Induced by A Type Weights. Potential Analysis, 50, 221-244.
https://doi.org/10.1007/s11118-018-9680-z
[11]  Bonet, J. and Taskinen, J. (2015) A Note about Volterra Operators on Weighted Banach Spaces of Entire Functions. Mathematische Nachrichten, 288, 1216-1225.
https://doi.org/10.1002/mana.201400099
[12]  Mengestie, T. (2015) Generalized Volterra Companion Operators on Fock Spaces. Potential Analysis, 44, 579-599.
https://doi.org/10.1007/s11118-015-9520-3
[13]  Mengestie, T. and Ueki, S. (2018) Integral, Differential and Multiplication Operators on Generalized Fock Spaces. Complex Analysis and Operator Theory, 13, 935-958.
https://doi.org/10.1007/s11785-018-0820-7

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133