PreprintCC BY 4.0arXiv
Littlewood-Paley and Carleson measure characterizations of Lipschitz spaces adapted to Schrödinger operators
Abstract
Let L =−Δ+V be a Schrödinger operator on ℝn, n ≥ 3, with the potential V being nonnegative and belonging to the reverse Hölder class RHq for some q >n/2. For 0< α<2, the Lipschitz space ΛLα(ℝn) adapted to L is defined as the space of all measurable functions f on ℝn such that |f|ΛLα:= |ρ(·)−αf(·)|L∞+ supz ∈ ℝn backslash {0} (|f(· + z) + f(· −z) −2 f(·)|L∞)/|z|α <∞, where ρ is the critical radius function related to L. In this paper, we provide characterizations of ΛαL(ℝn) in terms of Littlewood-Paley-type decompositions and Carleson measures, for 0< α< 2 −(n /q).
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BibTeX
@misc{hong2026littlewoodpaley,
title = {{Littlewood-Paley and Carleson measure characterizations of Lipschitz spaces adapted to Schrödinger operators}},
author = {Qing Hong and Yanfang Xu and Guorong Hu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.17434},
eprint = {2606.17434},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.17434},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Littlewood-Paley and Carleson measure characterizations of Lipschitz spaces adapted to Schrödinger operators
AU - Qing Hong
AU - Yanfang Xu
AU - Guorong Hu
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2606.17434
UR - https://arxiv.org/abs/2606.17434
AB - Let L =−Δ+V be a Schrödinger operator on ℝ^n, n ≥ 3, with the potential V being nonnegative and belonging to the reverse Hölder class RH_q for some q >n/2. For 0< α<2, the Lipschitz space Λ_L^α(ℝ^n) adapted to L is defined as the space of all measurable functions f on ℝ^n such that |f|_Λ_L^α:= |ρ(·)^−αf(·)|_L^∞+ sup_z ∈ ℝ^n backslash {0} (|f(· + z) + f(· −z) −2 f(·)|_L^∞)/|z|^α <∞, where ρ is the critical radius function related to L. In this paper, we provide characterizations of Λ^α_L(ℝ^n) in terms of Littlewood-Paley-type decompositions and Carleson measures, for 0< α< 2 −(n /q).
ER -