A Kuran Type Regularity Criterion for Sub-Laplacians: A Necessary and Sufficient Condition

Author: Tommasoli Andrea  

Publisher: Springer Publishing Company

ISSN: 0926-2601

Source: Potential Analysis, Vol.32, Iss.1, 2010-01, pp. : 57-66

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Abstract

The aim of this paper is to show the strong connection between regularity of bounded open set boundary points and quasi-boundedness, on the same set, of the fundamental solution of stratified Lie group sub-Laplacians. In the euclidean case the theorem was proved by Kuran (J Lond Math Soc 2(19):301–311, 1979). We later give two examples using some direct consequences of main theorem.