调和Fock空间上Toeplitz算子、Hankel算子和对偶Toeplitz算子间的乘积的有界性
Boundedness of the Products of Toeplitz Op-erators, Hankel Operators and Dual Toeplitz Operators on the Harmonic Fock Space
摘要: 本文主要刻画调和Fock空间上两个Toeplitz算子的乘积，Hankel算子与Toeplitz算子的乘积和对偶Toeplitz算子与Hankel算子的乘积的有界性。
Abstract: In this paper, we mainly characterize the boundedness of the product of two Toeplitz opera-tors, the product of Hankel operator and Toeplitz operator, and the product of dual Toeplitz operator and Hankel operator on harmonic Fock space.
文章引用：阚晶晶. 调和Fock空间上Toeplitz算子、Hankel算子和对偶Toeplitz算子间的乘积的有界性[J]. 应用数学进展, 2023, 12(1): 352-360. https://doi.org/10.12677/AAM.2023.121038

参考文献

[1] 洪颖. 调和Fock空间上的Toeplitz算子[D]: [硕士学位论文]. 长春: 东北师范大学, 2019.
[2] Sarason, D. (1994) Products of Toeplitzoperators. In: Linear and Complex Analysis Problem, Book 3, Part I, Lecture Notes in Math., Vol. 1573, Spring-Verlag, Berlin, 318-319.
[3] Sarason, D. (1989) Exposed Points in H1I. In: Dym, H., Goldberg, S., Kaashoek, M.A. and Lancaster, P., Eds., The Gohberg Anniversary Collection. Operator Theory: Advances and Applica-tions, Vol. 41, Birkhäuser Basel, 485-496. [Google Scholar] [CrossRef] 
[4] Sarason, D. (1990) Exposed Points in H1II. In: Dym, H., Goldberg, S., Kaashoek, M.A. and Lancaster, P., Eds., The Gohberg Anniversary Collection. Operator Theory: Advanc-es and Applications, Vol. 40/41, Birkhäuser, Basel, 333-347. [Google Scholar] [CrossRef] 
[5] Nazarov, F. (1997) A Counterexample to Sarason’s Conjec-ture. Preprint, MSU.
[6] Zheng, D.C. (1996) The Distribution Function in Equality and Products of Toeplitz Operators and Hankel Operators. Journal of Functional Analysis, 138, 477-501. [Google Scholar] [CrossRef] 
[7] Stroethoff, K. and Zheng, D. (1999) Products of Hankel and Toeplitz Operators on the Bergman Space. Journal of Functional Analysis, 169, 289-313. [Google Scholar] [CrossRef] 
[8] Stroethoff, K. and Zheng, D. (2003) Bounded Toeplitz Products on the Bergaman Space of the Polysisk. Journal of Mathematical Analysis and Applications, 278, 125-135. [Google Scholar] [CrossRef] 
[9] Stroethoff, K. and Zheng, D. (2007) Bounded Toeplitz Products on the Bergaman Spaces of the Unit Ball. Journal of Mathematical Analysis and Applications, 325, 114-129. [Google Scholar] [CrossRef] 
[10] Cho, H., Park, J. and Zhu, K. (2014) Products of Toeplitz Opera-tors on the Fockspace. Proceedings of the American Mathematical Society, 142, 2483-2489. [Google Scholar] [CrossRef] 
[11] Cho, H., Park, J. and Zhu, K. (2019) Products of Hankel Operators on the Fockspace. Journal of Functional Analysis, 277, 2644-2663. [Google Scholar] [CrossRef] 
[12] Ma, P., Yan, F., Zheng, D., et al. (2020) Mixed Products of Toeplitz and Hankel Operator on the Fockspace. Journal of Operator Theory, No. 1, 84.
[13] Bommier-Hato, H., Youssfi, E. and Zhu, K. (2017) Sarason’s Toeplitz Product Problem for a Class of Fockspaces. Bulletin des Sciences Mathématiques, 141, 408-442. [Google Scholar] [CrossRef] 
[14] Zhu, K. (2012) Analysis on Fockspace. Springer Science & Business Media, Berlin.

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