Abstract:Let $L =-\Delta +V$ be a Schrödinger operator on $\mathbb{R}^n$, $n \geq 3$, with the potential $V$ being nonnegative and belonging to the reverse Hölder class $RH_q$ for some $q >n/2$. For $0< \alpha <2$, the Lipschitz space $\Lambda_L^\alpha(\mathbb{R}^n)$ adapted to $L$ is defined as the space of all measurable functions $f$ on $\mathbb{R}^n$ such that \[ \|f\|_{\Lambda_L^\alpha}:= \|\rho(\cdot)^{-\alpha}f(\cdot)\|_{L^\infty}+ \sup_{z \in \mathbb{R}^n \backslash \{0\}}
\frac{\|f(\cdot + z) + f(\cdot -z) -2 f(\cdot)\|_{L^\infty}}{|z|^\alpha} <\infty, \] where $\rho$ is the critical radius function related to $L$. In this paper, we provide characterizations of $\Lambda^\alpha_L(\mathbb{R}^n)$ in terms of Littlewood-Paley-type decompositions and Carleson measures, for $0< \alpha < 2 -(n /q)$.
From: Guorong Hu [view email]
[v1]
Tue, 16 Jun 2026 02:34:00 UTC (22 KB)
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