PreprintCC BY 4.0arXiv
An interpretation of the BMO boundedness of Hörmander--Mikhlin multipliers
Abstract
We prove a pointwise domination of Poisson variances for Hörmander--Mikhlin multipliers on the real line. The estimate holds in operator order for operator-valued functions and gives a direct Fourier-side proof of BMO boundedness. The same argument gives an algebraic proof of the one-dimensional Schur multiplier estimate of Conde-Alonso, González-Pérez, Parcet and Tablate ( Annals of Mathematics, 2023), formulated here using Poisson BMO. The endpoint estimates are proved for L2 functions and Hilbert--Schmidt operators; interpolation gives the corresponding Lp and Schatten estimates.
Related
- Weak (1,1) Shur multipliers and the Hörmander--Mikhlin--Schur theorem
- Multilinear Mikhlin Multipliers with Degenerate Singularities
- A Remark on Hörmander Multipliers on Dunkl Hardy Spaces
- Kernel estimates for the Weyl-Hörmander calculus, Weak (1,1) boundedness and other regularity properties
- ℛ-boundedness of Riesz transforms and spectral multipliers of Schrödinger operators
BibTeX
@misc{mei2026interpretation,
title = {{An interpretation of the BMO boundedness of Hörmander--Mikhlin multipliers}},
author = {Tao Mei},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08192},
eprint = {2611.08192},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08192},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An interpretation of the BMO boundedness of Hörmander--Mikhlin multipliers
AU - Tao Mei
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08192
UR - https://arxiv.org/abs/2611.08192
AB - We prove a pointwise domination of Poisson variances for Hörmander--Mikhlin multipliers on the real line. The estimate holds in operator order for operator-valued functions and gives a direct Fourier-side proof of BMO boundedness. The same argument gives an algebraic proof of the one-dimensional Schur multiplier estimate of Conde-Alonso, González-Pérez, Parcet and Tablate ( Annals of Mathematics, 2023), formulated here using Poisson BMO. The endpoint estimates are proved for L^2 functions and Hilbert--Schmidt operators; interpolation gives the corresponding L^p and Schatten estimates.
ER -