PreprintarXiv licencearXiv
Endpoint Schatten class properties of commutators on quantum Euclidean spaces
Abstract
We study commutators [(−Δθ)ε/2,Mx] involving fractional Laplacians on quantum Euclidean spaces associated with arbitrary real antisymmetric matrices θ. For d≥2 and −d/2<ε≠ 0<1, we characterize critical weak Schatten class membership of [(−Δθ)ε/2,Mx] for any x as a tempered distribution by Sobolev spaces, with equivalent corresponding norms. We also establish precise asymptotics of singular values for [(−Δθ)ε/2,Mx]. For this purpose, we extend the Cwikel estimates and the required asymptotics of singular values to arbitrary real antisymmetric matrices, and we also establish a systematic approximation theory of tempered distributions on quantum Euclidean spaces.
Related
- Endpoint Schatten class properties of commutators on quantum tori
- Schatten--Lorentz properties of commutators with matrix weights
- Calderón Commutators on Quantum Euclidean Spaces and Quantum Tori
- Single commutators in Schatten ideals
- Schatten limits for semi-commutators in Toeplitz quantization on Fock space
BibTeX
@misc{pang2026endpoint,
title = {{Endpoint Schatten class properties of commutators on quantum Euclidean spaces}},
author = {Changbao Pang and Maofa Wang and Hao Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06405},
eprint = {2611.06405},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06405},
}
RIS
TY - UNPB
TI - Endpoint Schatten class properties of commutators on quantum Euclidean spaces
AU - Changbao Pang
AU - Maofa Wang
AU - Hao Zhang
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06405
UR - https://arxiv.org/abs/2611.06405
AB - We study commutators [(−Δ_θ)^ε/2,M_x] involving fractional Laplacians on quantum Euclidean spaces associated with arbitrary real antisymmetric matrices θ. For d≥2 and −d/2<ε≠ 0<1, we characterize critical weak Schatten class membership of [(−Δ_θ)^ε/2,M_x] for any x as a tempered distribution by Sobolev spaces, with equivalent corresponding norms. We also establish precise asymptotics of singular values for [(−Δ_θ)^ε/2,M_x]. For this purpose, we extend the Cwikel estimates and the required asymptotics of singular values to arbitrary real antisymmetric matrices, and we also establish a systematic approximation theory of tempered distributions on quantum Euclidean spaces.
ER -