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Fourier Spectrum Characterizations of Hp Spaces on Tubes Over Cones for 1 ≤ p≤ ∞
Hai-Chou Li1; Guan-Tie Deng2; Tao Qian3
2018-06-01
Source PublicationComplex Analysis and Operator Theory
ISSN1661-8262
Volume12Issue:5Pages:1193-1218
Abstract

We give Fourier spectrum characterizations of functions in the Hardy H spaces on tubes for 1 ≤ p≤ ∞. For F∈ L(R) , we show that F is the non-tangential boundary limit of a function in a Hardy space, H(T) , where Γ is an open cone of R and T is the related tube in C, if and only if the classical or the distributional Fourier transform of F is supported in Γ , where Γ is the dual cone of Γ. This generalizes the results of Stein and Weiss for p= 2 in the same context, as well as those of Qian et al. in one complex variable for 1 ≤ p≤ ∞. Furthermore, we extend the Poisson and Cauchy integral representation formulas to the H spaces on tubes for p∈ [ 1 , ∞] and p∈ [ 1 , ∞) , with, respectively, the two types of representations.

KeywordFourier Spectrum Fourier Transform Hardy Spaces Integral Representation Tube Domain
DOIhttp://doi.org/10.1007/s11785-017-0737-6
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000432152600003
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorTao Qian
Affiliation1.College of Mathematics and informatics, South China Agricultural University, Guangzhou, China
2.The First Institution, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
3.Department of Mathematics, University of Macau, Macao (Via Hong Kong), China
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Hai-Chou Li,Guan-Tie Deng,Tao Qian. Fourier Spectrum Characterizations of Hp Spaces on Tubes Over Cones for 1 ≤ p≤ ∞[J]. Complex Analysis and Operator Theory,2018,12(5):1193-1218.
APA Hai-Chou Li,Guan-Tie Deng,&Tao Qian.(2018).Fourier Spectrum Characterizations of Hp Spaces on Tubes Over Cones for 1 ≤ p≤ ∞.Complex Analysis and Operator Theory,12(5),1193-1218.
MLA Hai-Chou Li,et al."Fourier Spectrum Characterizations of Hp Spaces on Tubes Over Cones for 1 ≤ p≤ ∞".Complex Analysis and Operator Theory 12.5(2018):1193-1218.
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