A Poisson–Jensen Type Representation Formula for Subharmonic Functions on Stratified Lie Groups

Author： Bonfiglioli Andrea   Cinti Chiara  

Publisher： Springer Publishing Company

ISSN： 0926-2601

Source： Potential Analysis, Vol.22, Iss.2, 2005-03, pp. : 151-169

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

The aim of this paper is to prove a representation formula of Poisson–Jensen type on bounded domains Ω for subharmonic functions related to sub-Laplacians ∆G on stratified Lie groups G. Our result gives a complete answer to a question arisen in Math. Ann. 325 (2003), 97–122, where the additional hypothesis that Ω is regular for the Dirichlet problem related to ∆G was made: here we treat the case of arbitrary bounded domains Ω, omitting the hypothesis of regularity. In order to prove our representation formula, an ad-hoc theory of polar sets and capacity with respect to ∆G is also provided.

Related content

Gauge functions, Eikonal equations and Bôcher’s theorem on stratified Lie groups

By Bonfiglioli Andrea   Lanconelli Ermanno  

Calculus of Variations and Partial Differential Equations, Vol. 30, Iss. 3, 2007-11 ,pp. : 277-291 (15)

Springer Publishing Company

Access to resources Recommend Favorite

JENSEN TYPE INEQUALITIES FOR Q-CLASS FUNCTIONS

By  

Bulletin of the Australian Mathematical Society, Vol. 85, Iss. 1, 2011-10 ,pp. : 128-142 (15)

Cambridge University Press

Access to resources Recommend Favorite

Poisson transforms and mixed automorphic forms on semisimple Lie groups

By  

Bulletin of the Australian Mathematical Society, Vol. 61, Iss. 3, 2000-06 ,pp. : 353-370 (18)

Cambridge University Press

Access to resources Recommend Favorite

On the Self-Dual Representations of Finite Groups of Lie Type

By Prasad D.  

Journal of Algebra, Vol. 210, Iss. 1, 1998-12 ,pp. : 298-310 (13)

Academic Press

Access to resources Recommend Favorite

A Remark on Gelfand Pairs of Finite Groups of Lie Type

By Baruch E.M.   Feit S.W.  

Journal of Algebra, Vol. 201, Iss. 2, 1998-03 ,pp. : 493-500 (8)

Academic Press

Access to resources Recommend Favorite