KMS Of Academy of mathematics and systems sciences, CAS
Q(p) spaces on Riemann surfaces | |
Aulaskari, R; He, YZ; Ristioja, J; Zhao, RH | |
1998-06-01 | |
Source Publication | CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES |
ISSN | 0008-414X |
Volume | 50Issue:3Pages:449-464 |
Abstract | We 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 Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000074711500001 |
Publisher | CANADIAN MATHEMATICAL SOC |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/13326 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Aulaskari, R |
Affiliation | 1.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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