Fefferman--Stein type inequalities via area and maximal functions for Schrödinger operators with applications
Abstract
In this paper, we establish a Fefferman--Stein inequality in terms of area function and non-tangential maximal function associated with the Schrödinger operator ℒ = −Δ+ V on stratified Lie groups 𝒢, where Δ denotes the sub-Laplacian on 𝒢 and V is a nonnegative locally integrable function. As an application, we extend this inequality to the tensor product 𝒢1 × 𝒢2 of two stratified Lie groups and develop atomic decompositions associated with the Schrödinger operator for functions in the Orlicz space Llog+L(𝒢1 × 𝒢2). Using these atomic decompositions, we further prove weak-type endpoint estimates for the area integral operator and the Riesz transforms associated with the Schrödinger operator on Llog+L(𝒢1 × 𝒢2), thereby extending the celebrated result of R.\,Fefferman and E.M.\,Stein \cite{FSt1982} to the setting of singular integrals with non-smooth kernels.
Related
- Fefferman--Chang-type atomic decompositions for product Hardy spaces associated with Schrödinger operators
- Weighted norm inequalities for operators with new Muckenhoupt type weights in the Bessel setting and applications
- Capacitary domination and Fefferman--Phong inequalities for measure potentials on $2$-PI spaces
- KATO POTENTIALS AND SCHRÖDINGER OPERATORS ON LIE GROUPS
- Calderón problem for fractional Schrödinger operators on closed Riemannian manifolds
BibTeX
@misc{li2026feffermanstein,
title = {{Fefferman--Stein type inequalities via area and maximal functions for Schrödinger operators with applications}},
author = {Ji Li and Wanjun Li and Liang Song and Lixin Yan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08193},
eprint = {2609.08193},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08193},
}
RIS
TY - UNPB
TI - Fefferman--Stein type inequalities via area and maximal functions for Schrödinger operators with applications
AU - Ji Li
AU - Wanjun Li
AU - Liang Song
AU - Lixin Yan
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08193
UR - https://arxiv.org/abs/2609.08193
AB - In this paper, we establish a Fefferman--Stein inequality in terms of area function and non-tangential maximal function associated with the Schrödinger operator ℒ = −Δ+ V on stratified Lie groups 𝒢, where Δ denotes the sub-Laplacian on 𝒢 and V is a nonnegative locally integrable function. As an application, we extend this inequality to the tensor product 𝒢_1 × 𝒢_2 of two stratified Lie groups and develop atomic decompositions associated with the Schrödinger operator for functions in the Orlicz space Llog^+L(𝒢_1 × 𝒢_2). Using these atomic decompositions, we further prove weak-type endpoint estimates for the area integral operator and the Riesz transforms associated with the Schrödinger operator on Llog^+L(𝒢_1 × 𝒢_2), thereby extending the celebrated result of R.\,Fefferman and E.M.\,Stein \cite{FSt1982} to the setting of singular integrals with non-smooth kernels.
ER -