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Toeplitz operators between large Fock spaces

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In this paper, we give a complete characterization of the bounded and compact Toeplitz operators between different large Fock spaces \(F_\omega ^p\) and \(F_\omega ^q,\) with \(0<p,q\le \infty ,\) in terms of average functions, certain generalized Berezin transforms and Carleson measures. We characterize the essential norms of Toeplitz operators from \(F_\omega ^p\) into \(F_\omega ^q,\) for \(0<p,q\le \infty ,\) as well.

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The authors thank so much the editor and referee for the comments and suggestions that led to the improvement of the paper.

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Correspondence to Cezhong Tong.

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The authors declare that there is no conflict of interests regarding the publication of this paper.

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Communicated by Jose Bonet.

Tong was supported in part by Natural Science Foundation of Hebei Province (Grant No. A2020202005), Natural Science Foundation of Tianjin City (Grant No. 20JCYBJC00750) and Overseas Returnees Program of Hebei Province (Grant No. C201809).

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Arroussi, H., He, H., Li, J. et al. Toeplitz operators between large Fock spaces. Banach J. Math. Anal. 16, 32 (2022).

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