Sarason's Toeplitz product problem for a class of Fock spaces
Sarason's Toeplitz product problem for a class of Fock spaces
复制标题
DOI：
10.1016/j.bulsci.2017.03.002
复制
发表时间：
2017-07
影响因子：
1.3
通讯作者：
H. Bommier-Hato;E. Youssfi;Kehe Zhu
中科院分区：
文献类型：
--
作者：
H. Bommier-Hato;E. Youssfi;Kehe Zhu
Sarason的Toeplitz乘积问题问的是，当算子Tu Tv在各种解析函数的Hilbert空间上有界时，其中u和v是解析的。这个问题对于哈代空间和伯格曼空间上的Toeplitz算子是高度非平凡的（即使在单位圆盘的情况下）。本文给出了复平面上一类Fock空间的完全解。特别是，这推广了Cho，Park和Zhu的早期结果。
Sarason's Toeplitz product problem asks when the operator T u T v‾ is bounded on various Hilbert spaces of analytic functions, where u and v are analytic. The problem is highly nontrivial for Toeplitz operators on the Hardy space and the Bergman space (even in the case of the unit disk). In this paper, we provide a complete solution to the problem for a class of Fock spaces on the complex plane. In particular, this generalizes an earlier result of Cho, Park, and Zhu.