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Carleson Measures and Toeplitz Operators on Doubling Fock Spaces

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Abstract

Given ϕ a subharmonic function on the complex plane ℂ, with ΔϕdA being a doubling measure, the author studies Fock Carleson measures and some characterizations on μ such that the induced positive Toeplitz operator Tμ is bounded or compact between the doubling Fock space \(F_\phi ^p\) and \(F_\phi ^\infty \) with 0 < p ≤ ∞, where μ is a positive Borel measure on ℂ.

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Acknowledgement

The author would like to thank the referees for making some very good suggestions.

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Correspondence to Xiaofen Lv.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11601149, 11771139, 11571105) and the Zhejiang Provincial Natural Science Foundation of China (No. LY15A0 10014).

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Lv, X. Carleson Measures and Toeplitz Operators on Doubling Fock Spaces. Chin. Ann. Math. Ser. B 40, 349–362 (2019). https://doi.org/10.1007/s11401-019-0138-4

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  • DOI: https://doi.org/10.1007/s11401-019-0138-4

Keywords

2000 MR Subject Classification

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