PreprintCC BY 4.0arXiv
Berezin Transform Commutators
Abstract
We study commutators of Berezin transforms ℬα associated with radial weighted Fock spaces with exponential weights e−α|z|m on the complex plane. We prove that when m>2, the commutator [ℬα,ℬβ] is compact on the space L2(ℂ, dA) whenever α,β>0. We further show that if m>2 and α≠β, then the commutator is never of finite rank.
Related
- Compact Toeplitz operators via the Berezin transform on radial weighted Bergman spaces
- Endpoint Estimates for Commutators of the Dirichlet Riesz Transform on the Half-Space
- Convexity of the Berezin range of composition operators induced by automorphisms of the Unit Ball in ℂn
- Products of Berezin Transforms on Generalized Fock Spaces
- Berezin--Li--Yau inequalities for Aharonov--Bohm operators
BibTeX
@misc{borichev2026berezin,
title = {{Berezin Transform Commutators}},
author = {Alexander Borichev and Gérard Fantolini and El-Hassan Youssfi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33937},
eprint = {2610.33937},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33937},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Berezin Transform Commutators
AU - Alexander Borichev
AU - Gérard Fantolini
AU - El-Hassan Youssfi
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33937
UR - https://arxiv.org/abs/2610.33937
AB - We study commutators of Berezin transforms ℬ_α associated with radial weighted Fock spaces with exponential weights e^−α|z|^m on the complex plane. We prove that when m>2, the commutator [ℬ_α,ℬ_β] is compact on the space L^2(ℂ, dA) whenever α,β>0. We further show that if m>2 and α≠β, then the commutator is never of finite rank.
ER -