An atomic decomposition for hardy spaces associated to schrödinger operators

Liang Song; Chaoqiang Tan; Lixin Yan

doi:10.1017/S1446788711001376

An atomic decomposition for hardy spaces associated to schrödinger operators

Liang Song, Chaoqiang Tan^*, Lixin Yan

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Let L=-δ+V be a Schrödinger operator on R ⁿ where V is a nonnegative functionon in the space L ¹loc(R ⁿ) of locally integrable functions on R ⁿ. In this paper we provide an atomic decomposition for the Hardy space H ¹L(R ⁿ) associated to L in terms of the maximal function characterization. We then adapt our argument to give an atomic decomposition for the Hardy space H ¹L(R ⁿ×R ⁿ) on product domains.

Original language	English
Pages (from-to)	125-144
Number of pages	20
Journal	Journal of the Australian Mathematical Society
Volume	91
Issue number	1
DOIs	https://doi.org/10.1017/S1446788711001376
Publication status	Published - Aug 2011

Keywords

atom
nontangential maximal function
phrases Hardy space
product spaces
Schrödinger operator

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abstract = "Let L=-δ+V be a Schr{\"o}dinger operator on R n where V is a nonnegative functionon in the space L 1loc(R n) of locally integrable functions on R n. In this paper we provide an atomic decomposition for the Hardy space H 1L(R n) associated to L in terms of the maximal function characterization. We then adapt our argument to give an atomic decomposition for the Hardy space H 1L(R n×R n) on product domains.",

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author = "Liang Song and Chaoqiang Tan and Lixin Yan",

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AB - Let L=-δ+V be a Schrödinger operator on R n where V is a nonnegative functionon in the space L 1loc(R n) of locally integrable functions on R n. In this paper we provide an atomic decomposition for the Hardy space H 1L(R n) associated to L in terms of the maximal function characterization. We then adapt our argument to give an atomic decomposition for the Hardy space H 1L(R n×R n) on product domains.

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KW - nontangential maximal function

KW - phrases Hardy space

KW - product spaces

KW - Schrödinger operator

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An atomic decomposition for hardy spaces associated to schrödinger operators

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