SQUARE MEANS VERSUS DIRICHLET INTEGRALS FOR HARMONIC FUNCTIONS ON RIEMANN SURFACES

DOI 参考文献11件

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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.

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詳細情報 詳細情報について

  • CRID
    1390282680094242048
  • NII論文ID
    130005128511
  • DOI
    10.2748/tmj/1341249373
  • ISSN
    2186585X
    00408735
  • 本文言語コード
    en
  • データソース種別
    • JaLC
    • Crossref
    • CiNii Articles
  • 抄録ライセンスフラグ
    使用不可

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