CSpace
Q(p) spaces on Riemann surfaces
Aulaskari, R; He, YZ; Ristioja, J; Zhao, RH
1998-06-01
Source PublicationCANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
ISSN0008-414X
Volume50Issue:3Pages:449-464
AbstractWe study the function spaces Q(p)(R) defined on a Riemann surface R, which were earlier introduced in the unit disk of the complex plane. The nesting property Q(p)(R) subset of or equal to Q(q)(R) for 0 < p < q < infinity is shown in case of arbitrary hyperbolic Riemann surfaces. Further, it is proved that the classical Dirichlet space AD(R) subset of or equal to Q(p)(R) for any p, 0 < p < infinity, thus sharpening T. Metzger's well-known result AD(R) subset of or equal to BMOA(R). Also the first author's result AD(R) subset of or equal to VMOA(R) for a regular Riemann surface R is sharpened by showing that, in fact, AD(R) subset of or equal to Q(p,0)(R) for all p, 0 < p < infinity. The relationships between ep(R) and various generalizations of the Bloch space on R are considered. Finally we show that Q(p)(R) is a Banach space for 0 < p < infinity.
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000074711500001
PublisherCANADIAN MATHEMATICAL SOC
Citation statistics
Cited Times:11[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/13326
Collection中国科学院数学与系统科学研究院
Affiliation1.Univ Joensuu, Dept Math, FIN-80101 Joensuu, Finland
2.Acad Sinica, Inst Math, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Aulaskari, R,He, YZ,Ristioja, J,et al. Q(p) spaces on Riemann surfaces[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,1998,50(3):449-464.
APA Aulaskari, R,He, YZ,Ristioja, J,&Zhao, RH.(1998).Q(p) spaces on Riemann surfaces.CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,50(3),449-464.
MLA Aulaskari, R,et al."Q(p) spaces on Riemann surfaces".CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES 50.3(1998):449-464.
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