PreprintCC BY 4.0arXiv
Two-parameter Toeplitz-type operators between Fock spaces
Abstract
We introduce and study a two-parameter family of Toeplitz-type operators T(s,t)φ on the Fock space Fp(C) for 0<p≤∞. For all 0<p, q ≤∞ we obtain sharp conditions for φ such that T(s,t)φ: Fp(C)→ Fq(C) is bounded or compact. In the Hilbert space case T(s,t)φ: F2(C)→ F2(C), we also study the Berezin transform of T(s,t)φ and membership of T(s,t)φ in Schatten classes. Furthermore, we find a class of noncompact operators whose Berezin transforms nevertheless vanish at infinity.
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BibTeX
@misc{dong2026twoparameter,
title = {{Two-parameter Toeplitz-type operators between Fock spaces}},
author = {Xingtang Dong and Zipeng Wang and Kehe Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24318},
eprint = {2610.24318},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24318},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Two-parameter Toeplitz-type operators between Fock spaces
AU - Xingtang Dong
AU - Zipeng Wang
AU - Kehe Zhu
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24318
UR - https://arxiv.org/abs/2610.24318
AB - We introduce and study a two-parameter family of Toeplitz-type operators T^(s,t)_φ on the Fock space F^p(C) for 0<p≤∞. For all 0<p, q ≤∞ we obtain sharp conditions for φ such that T^(s,t)_φ: F^p(C)→ F^q(C) is bounded or compact. In the Hilbert space case T^(s,t)_φ: F^2(C)→ F^2(C), we also study the Berezin transform of T^(s,t)_φ and membership of T^(s,t)_φ in Schatten classes. Furthermore, we find a class of noncompact operators whose Berezin transforms nevertheless vanish at infinity.
ER -