TY - JOUR

T1 - Properties of harmonic measures in the Dirichlet problem for nilpotent lie groups of Heisenberg type

AU - Capogna, Luca

AU - Garofalo, Nicola

AU - Nhieu, Duy Minh

PY - 2002

Y1 - 2002

N2 - In groups of Heisenberg type we introduce a large class of domains, which we call ADP, admissible for the Dirichlet problem, and we prove that on the boundary of such domains, harmonic measure, ordinary surface measure, and the perimeter measure, are mutually absolutely continuous. We also establish the solvability of the Dirichlet problem when the boundary datum belongs to LP, 1 < p ≤ ∞, with respect to the ordinary surface measure. Here, the harmonic measure is that relative to a sub-Laplacian associated with a basis of the first layer of the Lie algebra. A domain is called ADP if it is a nontangentially accessible domain and it satisfies an intrinsic outer ball condition.

AB - In groups of Heisenberg type we introduce a large class of domains, which we call ADP, admissible for the Dirichlet problem, and we prove that on the boundary of such domains, harmonic measure, ordinary surface measure, and the perimeter measure, are mutually absolutely continuous. We also establish the solvability of the Dirichlet problem when the boundary datum belongs to LP, 1 < p ≤ ∞, with respect to the ordinary surface measure. Here, the harmonic measure is that relative to a sub-Laplacian associated with a basis of the first layer of the Lie algebra. A domain is called ADP if it is a nontangentially accessible domain and it satisfies an intrinsic outer ball condition.

UR - http://www.scopus.com/inward/record.url?scp=0036327887&partnerID=8YFLogxK

U2 - 10.1353/ajm.2002.0010

DO - 10.1353/ajm.2002.0010

M3 - 期刊論文

AN - SCOPUS:0036327887

VL - 124

SP - 273

EP - 306

JO - American Journal of Mathematics

JF - American Journal of Mathematics

SN - 0002-9327

IS - 2

ER -