Fredholm Toeplitz operators with VMO symbols and the duality of generalized Fock spaces with small exponents

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 o...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2020-12, Vol.150 (6), p.3163-3186
Main Authors: Hu, Zhangjian, Virtanen, Jani A.
Format: Article
Language:English
Subjects:
Exponents
Function space
Operators (mathematics)
Symbols
Weighting functions
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Summary: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.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2019.65