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Potential theory in conical domains. II

Published online by Cambridge University Press:  16 October 2000

N. Th. VAROPOULOS
N. Th. VAROPOULOS
Affiliation:
Department of Mathematics, Universite Paris IV et Institut Universitate de France, 75252, Paris Cedex 05, France
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Abstract

0·1. Conical domains

The aim of this paper is to improve the results of my previous work in the area [1]. Let us start by recalling some of the notations and definitions of [1].

Let Ω ⊂ ℝd be some convex open cone with vertex at 0 such that [emptyv ] &≠; Ω &≠; ℝd. Let u ∈ C(Ω) be the reduite, i.e.

formula here

and let α = degΩ[ges ] 1 be the homogeneity degree of u. Let us consider the random walk

formula here

controlled by some compactly supported measure

formula here

that is centred with covarience = I, i.e.

formula here

We then denote:

formula here

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 129 , Issue 2 , September 2000 , pp. 301 - 320
Copyright
2000 Cambridge Philosophical Society

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