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AN ATOMIC DECOMPOSITION FOR HARDY SPACES ASSOCIATED TO SCHRÖDINGER OPERATORS

Part of: Harmonic analysis in several variables Partial differential operators

Published online by Cambridge University Press:  28 September 2011

LIANG SONG ,
CHAOQIANG TAN  and
LIXIN YAN
LIANG SONG
Affiliation:
Department of Mathematics, Sun Yat-sen (Zhongshan) University, Guangzhou 510275, PR China (email: songl@mail.sysu.edu.cn)
CHAOQIANG TAN*
Affiliation:
Department of Mathematics, Shantou University, Shantou Guangdong 515063, PR China (email: cqtan@stu.edu.cn)
LIXIN YAN
Affiliation:
Department of Mathematics, Sun Yat-sen (Zhongshan) University, Guangzhou 510275, PR China (email: mcsylx@mail.sysu.edu.cn)
*
✉For correspondence; e-mail: cqtan@stu.edu.cn
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Abstract

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Let L=−Δ+V be a Schrödinger operator on ℝn where V is a nonnegative function in the space L1loc(ℝn) of locally integrable functions on ℝn. In this paper we provide an atomic decomposition for the Hardy space H1L(ℝn) associated to L in terms of the maximal function characterization. We then adapt our argument to give an atomic decomposition for the Hardy space H1L(ℝn×ℝn) on product domains.

Keywords

Hardy spaceSchrödinger operatoratomnontangential maximal functionproduct spaces

MSC classification

Secondary: 42B30: $H^p$-spaces 47F05: Partial differential operators (should also be assigned at least one other classification number in section 47)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 1 , August 2011 , pp. 125 - 144
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

L. Song is supported by NNSF of China (No. 11001276 and 10926136) and NSF of Guangdong (No. 9451027501002491). C. Q. Tan is supported by NNSF of China (No. 11026215), NSF of Guangdong (No. 10451503101006384) and Specialized Research Fund for the Doctoral Program of Higher Education (No. 20104402120002). L. X. Yan is supported by NNSF of China (No. 10771221 and 10925106).

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