The 3G inequality for a uniformly John domain

• Aikawa Hiroaki

• Lundh Torbjörn

抄録

Let G be the Green function for a domain D⊂R^d with d≥3. The Martin boundary of D and the 3G inequality:<BR>\frac{G(x, y)G(y, z)}{G(x, z)}≤A(|x−y|^2−d+|y−z|^2−d)   for x, y, z∈D<BR>are studied. We give the 3G inequality for a bounded uniformly John domain D, although the Martin boundary of D need not coincide with the Euclidean boundary. On the other hand, we construct a bounded domain such that the Martin boundary coincides with the Euclidean boundary and yet the 3G inequality does not hold.

収録刊行物

• ＫＯＤＡＩ　ＭＡＴＨＥＭＡＴＩＣＡＬ　ＪＯＵＲＮＡＬ

  ＫＯＤＡＩ　ＭＡＴＨＥＭＡＴＩＣＡＬ　ＪＯＵＲＮＡＬ 28 (2), 209-219, 2005

  国立大学法人 東京工業大学理学院数学系

キーワード

• General Mathematics

詳細情報

• CRID: 1390282680248391424
• NII論文ID: 130003574484
• DOI: 10.2996/kmj/1123767003
• ISSN: 18815472
• ISSN: 03865991
• MRID: 2153910
• 本文言語コード: en
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