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Summer 2019 Atomic characterizations of Hardy spaces associated to Schrödinger type operators
Junqiang Zhang, Zongguang Liu
Adv. Oper. Theory 4(3): 604-624 (Summer 2019). DOI: 10.15352/aot.1811-1440

Abstract

‎In this article‎, ‎the authors consider the Schrödinger type‎ ‎operator $L:=-{\rm div}(A\nabla)+V$ on $\mathbb{R}^n$ with $n\geq 3$‎, ‎where the matrix $A$ is symmetric and satisfies‎ ‎the uniformly elliptic condition and the nonnegative potential‎ ‎$V$ belongs to the reverse Hölder class $RH_q(\mathbb{R}^n)$‎ ‎with $q\in(n/2,\,\infty)$‎. ‎Let $p(\cdot):\ \mathbb{R}^n\to(0,\,1]$ be a variable exponent function‎ ‎satisfying the globally $\log$-Hölder continuous condition‎. ‎The authors introduce the variable Hardy space $H_L^{p(\cdot)}(\mathbb{R}^n)$ associated to $L$‎ ‎and establish its atomic characterization‎. ‎The atoms here are closer to the atoms of‎ ‎variable Hardy space $H^{p(\cdot)}(\mathbb{R}^n)$ in spirit‎, ‎which further implies that $H^{p(\cdot)}(\mathbb{R}^n)$ is continuously embedded in‎ ‎$H_L^{p(\cdot)}(\mathbb{R}^n)$‎.

Citation

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Junqiang Zhang. Zongguang Liu. "Atomic characterizations of Hardy spaces associated to Schrödinger type operators." Adv. Oper. Theory 4 (3) 604 - 624, Summer 2019. https://doi.org/10.15352/aot.1811-1440

Information

Received: 27 November 2018; Accepted: 19 December 2018; Published: Summer 2019
First available in Project Euclid: 2 March 2019

zbMATH: 07056788
MathSciNet: MR3919034
Digital Object Identifier: 10.15352/aot.1811-1440

Subjects:
Primary: 42B30
Secondary: 35J10, 42B35

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 3 • Summer 2019
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