Volume 31, Issue 2
Hardy Spaces $H^p_L(\mathbb{R}^n)$ Associated with Higher-Order Schrödinger Type Operators

Anal. Theory Appl., 31 (2015), pp. 184-206.

Published online: 2017-04

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• 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 $e^{−tL}$.

• Keywords

Higher order Schrödinger operator, off-diagonal estimates, $H^p_L$ spaces, area integrals.

42B30, 42B25, 42B35, 35J15

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@Article{ATA-31-184, author = {}, title = {Hardy Spaces $H^p_L(\mathbb{R}^n)$ Associated with Higher-Order Schrödinger Type Operators}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {31}, number = {2}, pages = {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 $e^{−tL}$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2015.v31.n2.8}, url = {http://global-sci.org/intro/article_detail/ata/4633.html} }
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 -

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 $e^{−tL}$.

Q. Deng, Y. Ding & X. Yao. (1970). Hardy Spaces $H^p_L(\mathbb{R}^n)$ Associated with Higher-Order Schrödinger Type Operators. Analysis in Theory and Applications. 31 (2). 184-206. doi:10.4208/ata.2015.v31.n2.8
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