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MUTUAL ABSOLUTE CONTINUITY OF HARMONIC AND SURFACE MEASURES FOR HÖRMANDER TYPE OPERATORS

By Luca Capogna, Nicola Garofalo and Duy-minh Nhieu

Abstract

In this paper we study the Dirichlet problem for the sub-Laplacian associated with a system X = {X1,...,Xm} of C ∞ real vector fields in R n satisfying Hörmander’s finite rank condition (1.1) rank Lie[X1,...,Xm] ≡ n. Throughout this paper n ≥ 3, and X ∗ j denotes the formal adjoint of Xj. The sub-Laplacia

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