Year: 2015
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 2 : pp. 184–206
Abstract
Let $L = L_0+V$ be the higher order Schrödinger type operator where $L_0$ is a homogeneous elliptic operator of order $2m$ in divergence form with bounded coefficients and $V$ is a real measurable function as multiplication operator (e.g., including $(−∆) ^m+V (m∈\mathbb{N})$ as special examples). In this paper, assume that $V$ satisfies a strongly subcritical form condition associated with $L_0$, the authors attempt to establish a theory of Hardy space $H^p_L(\mathbb{R}^n) (0 < p ≤ 1)$ associated with the higher order Schrödinger type operator $L$. Specifically, we first define the molecular Hardy space $H^p_L(\mathbb{R}^n)$ by the so-called $(p,q,ε,M)$ molecule associated to $L$ and then establish its characterizations by the area integral defined by the heat semigroup $e^{−tL}$.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2015.v31.n2.8
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 2 : pp. 184–206
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Higher order Schrödinger operator off-diagonal estimates $H^p_L$ spaces area integrals.
-
The boundedness of area integrals associated with operators on product domains
Juan, Song
Qingquan, Deng
SCIENTIA SINICA Mathematica, Vol. 54 (2024), Iss. 1 P.59
https://doi.org/10.1360/SSM-2023-0234 [Citations: 0]