Phi-HARMONIC FUNCTIONS ON DISCRETE GROUPS AND THE FIRST l(Phi)-COHOMOLOGY

作者：Kopylov Ya A^*; Panenko R A

来源：Siberian Mathematical Journal, 2014, 55(5): 904-914.

DOI：10.1134/S0037446614050097

• group
• N-function
• Orlicz space
• Delta(2)-regularity
• Phi-harmonic function
• 1-cohomology

We study the first cohomology groups of a countable discrete group G with coefficients in a G-module a""(I broken vertical bar)(G), where I broken vertical bar is an N-function of class Delta(2)(0) a (c) a-(2)(0). Developing the ideas of Puls and Martin-Valette for a finitely generated group G, we introduce the discrete I broken vertical bar-Laplacian and prove a theorem on the decomposition of the space of I broken vertical bar-Dirichlet finite functions into the direct sum of the spaces of I broken vertical bar-harmonic functions and a""(I broken vertical bar)(G) (with an appropriate factorization). We prove also that if a finitely generated group G has a finitely generated infinite amenable subgroup with infinite centralizer then (G, a""(I broken vertical bar)(G)) = 0. In conclusion, we show the triviality of the first cohomology group for the wreath product of two groups one of which is nonamenable.

• 出版日期2014-9