TY - JOUR
T1 - Hardy Spaces $H^p_L(\mathbb{R}^n)$ Associated with Higher-Order Schrödinger Type Operators
JO - Analysis in Theory and Applications
VL - 2
SP - 184
EP - 206
PY - 2017
DA - 2017/04
SN - 31
DO - http://doi.org/10.4208/ata.2015.v31.n2.8
UR - https://global-sci.org/intro/article_detail/ata/4633.html
KW - Higher order Schrödinger operator, off-diagonal estimates, $H^p_L$ spaces, area integrals.
AB - <p style="text-align: justify;">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 $H^p_L(\mathbb{R}^n) (0 &lt; p ≤ 1)$ 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 $e^{−tL}$.</p>