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AN ATOMIC DECOMPOSITION FOR HARDY SPACES ASSOCIATED TO SCHRÖDINGER OPERATORS

Published online by Cambridge University Press:  28 September 2011

LIANG SONG
Affiliation:
Department of Mathematics, Sun Yat-sen (Zhongshan) University, Guangzhou 510275, PR China (email: [email protected])
CHAOQIANG TAN*
Affiliation:
Department of Mathematics, Shantou University, Shantou Guangdong 515063, PR China (email: [email protected])
LIXIN YAN
Affiliation:
Department of Mathematics, Sun Yat-sen (Zhongshan) University, Guangzhou 510275, PR China (email: [email protected])
*
For correspondence; e-mail: [email protected]
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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.

Type
Research Article
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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