IDA symbols and Schatten--Lorentz theory for Toeplitz operators on weighted Fock spaces
Abstract
We study complex-symbol Toeplitz operators on weighted Fock spaces. The weight has a uniformly positive and bounded real Hessian. Local analytic distance is unchanged when an entire function is added to the symbol. We combine this distance with a complex ball average or the Berezin transform to control the local size of the symbol. Under a matching Lorentz condition on the distance, we characterize membership in every Schatten--Lorentz class. The local symbol exponent can be any 1≤ q<∞ and is independent of the two Schatten--Lorentz indices. The proof uses positive Toeplitz estimates, Hankel estimates, and a local decomposition that preserves the initial domain. Two examples show why the local exponent and the secondary Lorentz index must be kept. We also obtain mixed mapping criteria and regular singular-value decay estimates. An error operator with a lower-order counting function does not change the leading coefficient. This gives explicit Weyl constants for quadratic weights. A radial example shows that uniform Hessian bounds alone do not imply such a constant.
Related
- Hyponormal Toeplitz operators with operator valued normal symbols
- Commuting Toeplitz operators with harmonic symbols on the Fock space
- The spectral structure of Toeplitz operators with polynomial symbols on the harmonic Bergman space
- Zero products of Toeplitz operators with harmonic symbols on the Bergman space of the unit ball
- Small exponent Schatten class Toeplitz operators on convex domains of finite type
BibTeX
@misc{chunxu2026symbols,
title = {{IDA symbols and Schatten--Lorentz theory for Toeplitz operators on weighted Fock spaces}},
author = {Xu Chunxu and Dong Jianxiang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16970},
eprint = {2609.16970},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16970},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - IDA symbols and Schatten--Lorentz theory for Toeplitz operators on weighted Fock spaces
AU - Xu Chunxu
AU - Dong Jianxiang
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16970
UR - https://arxiv.org/abs/2609.16970
AB - We study complex-symbol Toeplitz operators on weighted Fock spaces. The weight has a uniformly positive and bounded real Hessian. Local analytic distance is unchanged when an entire function is added to the symbol. We combine this distance with a complex ball average or the Berezin transform to control the local size of the symbol. Under a matching Lorentz condition on the distance, we characterize membership in every Schatten--Lorentz class. The local symbol exponent can be any 1≤ q<∞ and is independent of the two Schatten--Lorentz indices. The proof uses positive Toeplitz estimates, Hankel estimates, and a local decomposition that preserves the initial domain. Two examples show why the local exponent and the secondary Lorentz index must be kept. We also obtain mixed mapping criteria and regular singular-value decay estimates. An error operator with a lower-order counting function does not change the leading coefficient. This gives explicit Weyl constants for quadratic weights. A radial example shows that uniform Hessian bounds alone do not imply such a constant.
ER -