Hardy space decomposition of L-p on the unit circle: 0 < p <= 1
Hai-Chou Li1; Guan-Tie Deng2; Tao Qian1
Source PublicationComplex Variables and Elliptic Equations
ISSN17476941 17476933

In this paper we consider Hardy space decomposition of (Formula presented.) where (Formula presented.) stands for the open unit disc, and (Formula presented.) is its boundary. Hardy spaces decompositions for (Formula presented.) and (Formula presented.) for (Formula presented.) are, as classical results, available in the literature. For (Formula presented.) the basic tools are the Plemelj formula and the boundedness of the Hilbert transformation. For (Formula presented.) neither on the real line, nor on the unit circle, a Plemelj formula, or Hilbert transformation are available. In a recent paper Deng and Qian obtain Hardy spaces decomposition for (Formula presented.) on the real line by means of rational approximation. In the present paper by using rational functions, we achieve the same goal for (Formula presented.) for the range (Formula presented.) The work on the unit circle exposes the particular features of the kind of decomposition in the compact situation adaptable to higher dimensions.

KeywordAnalytic Signal Decomposition Theorem Hardy Space Rational Approximation Unit Disc
URLView the original
Indexed BySCIE
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000372019700007
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Cited Times [WOS]:4   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorGuan-Tie Deng
Affiliation1.Department of Mathematics, University of Macau, Macao
2.School of Mathematical Sciences, Beijing Normal University, Beijing
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Hai-Chou Li,Guan-Tie Deng,Tao Qian. Hardy space decomposition of L-p on the unit circle: 0 < p <= 1[J]. Complex Variables and Elliptic Equations,2016,61(4):510-523.
APA Hai-Chou Li,Guan-Tie Deng,&Tao Qian.(2016).Hardy space decomposition of L-p on the unit circle: 0 < p <= 1.Complex Variables and Elliptic Equations,61(4),510-523.
MLA Hai-Chou Li,et al."Hardy space decomposition of L-p on the unit circle: 0 < p <= 1".Complex Variables and Elliptic Equations 61.4(2016):510-523.
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