Positive Toeplitz Operators Between Gaussian Mixed-Norm Fock Spaces
Abstract
We study positive measure-symbol Toeplitz operators between Gaussian radial--angular mixed-norm Fock spaces throughout the full range of exponents, including infinity. We obtain a complete characterization of boundedness in terms of weighted local masses of the symbol measure, or equivalently in terms of its Gaussian Berezin profile. The criterion separates the transfer of angular integrability from that of radial summability and remains valid in the quasi-Banach and endpoint regimes. We further characterize compactness and obtain the corresponding essential-norm estimates through the asymptotic behavior of the same local-mass and Berezin profiles, and determine the mappings involving the large and little outer-endpoint spaces. We also prove an independent characterization of bounded positive Toeplitz sesquilinear forms. The proofs combine atomic recovery, localized Gaussian matrix estimates, and Rademacher extraction.
Related
- Comparing positive Toeplitz operators on holomorphic and pluriharmonic Fock spaces
- Two-parameter Toeplitz-type operators between Fock spaces
- Toeplitz and Hankel operators on Bergman spaces with doubling weights
- Absolutely summing Toeplitz operators on weighted Fock spaces
- Compact Toeplitz operators via the Berezin transform on radial weighted Bergman spaces
BibTeX
@misc{dileep2026positive,
title = {{Positive Toeplitz Operators Between Gaussian Mixed-Norm Fock Spaces}},
author = {Deepak K. Dileep and Xiang Fang and Pham Trong Tien},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40236},
eprint = {2610.40236},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40236},
}
RIS
TY - UNPB
TI - Positive Toeplitz Operators Between Gaussian Mixed-Norm Fock Spaces
AU - Deepak K. Dileep
AU - Xiang Fang
AU - Pham Trong Tien
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40236
UR - https://arxiv.org/abs/2610.40236
AB - We study positive measure-symbol Toeplitz operators between Gaussian radial--angular mixed-norm Fock spaces throughout the full range of exponents, including infinity. We obtain a complete characterization of boundedness in terms of weighted local masses of the symbol measure, or equivalently in terms of its Gaussian Berezin profile. The criterion separates the transfer of angular integrability from that of radial summability and remains valid in the quasi-Banach and endpoint regimes. We further characterize compactness and obtain the corresponding essential-norm estimates through the asymptotic behavior of the same local-mass and Berezin profiles, and determine the mappings involving the large and little outer-endpoint spaces. We also prove an independent characterization of bounded positive Toeplitz sesquilinear forms. The proofs combine atomic recovery, localized Gaussian matrix estimates, and Rademacher extraction.
ER -