SQUARE MEANS VERSUS DIRICHLET INTEGRALS FOR HARMONIC FUNCTIONS ON RIEMANN SURFACES
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- MASAOKA HIROAKI
- Department of Mathematics, Faculty of Science, Kyoto Sangyou University
Abstract
We show rather unexpectedly and surprisingly the existence of a hyperbolic Riemann surface $W$ enjoying the following two properties: firstly, the converse of the celebrated Parreau inclusion relation that the harmonic Hardy space $HM_2(W)$ with exponent 2 consisting of square mean bounded harmonic functions on $W$ includes the space $HD(W)$ of Dirichlet finite harmonic functions on $W$, and a fortiori $HM_2(W)=HD(W)$, is valid; secondly, the linear dimension of $HM_2(W)$, hence also that of $HD(W)$, is infinite.
Journal
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- Tohoku Mathematical Journal, Second Series
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Tohoku Mathematical Journal, Second Series 64 (2), 233-259, 2012
Mathematical Institute, Tohoku University
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Keywords
Details 詳細情報について
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- CRID
- 1390282680094242048
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- NII Article ID
- 130005128511
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- ISSN
- 2186585X
- 00408735
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- Text Lang
- en
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- Data Source
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- JaLC
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed