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

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

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 $e^{−tL}$.

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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.

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