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Fredholm Toeplitz operators with VMO symbols and the duality of generalized Fock spaces with small exponents
Proceedings of the Royal Society of Edinburgh Section A: Mathematics ( IF 1.3 ) Pub Date : 2019-12-03 , DOI: 10.1017/prm.2019.65
Zhangjian Hu , Jani A. Virtanen

We characterize Fredholmness of Toeplitz operators acting on generalized Fock spaces of the n-dimensional complex space for symbols in the space of vanishing mean oscillation VMO. Our results extend the recent characterizations for Toeplitz operators on standard weighted Fock spaces to the setting of generalized weight functions and also allow for unbounded symbols in VMO for the first time. Another novelty is the treatment of small exponents 0 < p < 1, which to our knowledge has not been seen previously in the study of the Fredholm properties of Toeplitz operators on any function spaces. We accomplish this by describing the dual of the generalized Fock spaces with small exponents.

中文翻译:

具有 VMO 符号的 Fredholm Toeplitz 算子和具有小指数的广义 Fock 空间的对偶性

我们描述了作用于广义 Fock 空间的 Toeplitz 算子的 Fredholmnessn维数复空间,用于消失平均振荡 VMO 空间中的符号。我们的结果将标准加权 Fock 空间上 Toeplitz 算子的最新表征扩展到广义权重函数的设置,并且还首次允许在 VMO 中使用无界符号。另一个新颖之处是小指数的处理 0 <p< 1,据我们所知,以前在任何函数空间上的 Toeplitz 算子的 Fredholm 属性的研究中都没有看到过。我们通过描述具有小指数的广义 Fock 空间的对偶来实现这一点。
更新日期:2019-12-03
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