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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 11: Functional theoretic methods, wavelets and applied PDEs on the occasion of Professor Wei Lin’s 80th Birthday and the 30th anniversary of Robert Gilbert visiting China. Guest editors Daoqing Dai, Yuqiu Zhao and Yongzhi Steve Xu
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Articles

Spaces of harmonic functions with boundary values in

Qixiang YangSchool of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China.
,
Tao QianFaculty of Science and Technology, Department of Mathematics, University of Macau, Macau, China.
&
Pengtao LiCollege of Mathematics, Qingdao University, Qingdao, Shandong, 266071, China.Correspondence[email protected]
Pages 2498-2518 | Received 25 Aug 2014, Accepted 26 Aug 2014, Published online: 07 Oct 2014
 
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Abstract

In this paper, we apply wavelets to study two classes of function spaces of harmonic functions: the weighted Besov spaces and Carleson spaces . By a reproducing formula, we prove that the elements in these harmonic function spaces can be characterized by the Poisson integral of the functions in the Besov-Q spaces .

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Notes

Pengtao Li’s research is supported by NSFC [grant number 11171203], [grant number 11201280]; New Teacher’s Fund for Doctor Stations, Ministry of Education [grant number 20114402120003]; Foundation for Distinguished Young Talents in Higher Education of Guangdong, China, LYM11063. Qixiang Yang’s research is supported in part by NSFC [grant number 11271209]. Tao Qian’s research is supported in part by MYRG116(Y1-L3)-FST13- QT; MYRG115(Y1-L4)-FST13-QT; and FDCT 098/2012/A3.

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