上半空間での正値調和関数について

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書誌事項

タイトル別名
  • On positive harmonic functions in the upper half space
  • 〓

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抄録

In the n(≧2)-dimensional Euclidean (ξ)=(ξ_1.…, ξ_n) space, let v (ξ) be a positive harmonic function in the upper half space G : ξ_n>0 and H be the boundary of G, that is, the hyperplane ξ_n=0. Then, denoting by η=(η_1,…, η_<n-1>, 0) the points of the plane H, there exists a non-negative mass distribution υin H and a constant c≧0 such that [numerical formula] where [numerical formula] denotes the surface area of the unit sphere [numerical formula] In this note, we shall present, in §3,a new proof of the above formula (*), which is entirely different from the original proof and seems to be more simple and more natural as compared with the original one. Moreover, as its application, we shall give, in §5,a extremely brief proof for the classical but epoch-making Fatou's therem in the theory of analytic functions and, by means of the real function-theoretic arguments, we shall give, in §6,a delicate variant of the Reflection Princiole due to H. Schwarz. The first two sections 1 and 2 give the prelimiaries for the following treatments.

identifier:5

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詳細情報 詳細情報について

  • CRID
    1050564288197152768
  • NII論文ID
    110000187675
  • NII書誌ID
    AN0011586X
  • ISSN
    09160175
  • Web Site
    http://id.nii.ac.jp/1550/00001680/
  • 本文言語コード
    ja
  • 資料種別
    departmental bulletin paper
  • データソース種別
    • IRDB
    • CiNii Articles

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