Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An area theorem for a one-dimensional semidirect extension of homogeneous groups


Author: Ewa Damek
Journal: Proc. Amer. Math. Soc. 104 (1988), 1279-1283
MSC: Primary 22E30; Secondary 43A80, 43A85
DOI: https://doi.org/10.1090/S0002-9939-1988-0969058-X
MathSciNet review: 969058
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ N$ be a homogeneous group [3] and let $ \{ {\delta _a}:a \in A = {R^ + }\} $ be the group of dilations of $ N$. We prove an area theorem for harmonic functions w.r.t. a class of second-order left-invariant hypoelliptic differential operators $ L$ on the semidirect product $ S = NA$ with $ ax{a^{ - 1}} = {\delta _a}(x),a \in A,x \in N$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22E30, 43A80, 43A85

Retrieve articles in all journals with MSC: 22E30, 43A80, 43A85


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0969058-X
Keywords: Area theorem, left-invariant operators, homogeneous groups
Article copyright: © Copyright 1988 American Mathematical Society