Affiliation:
1. Dipartimento d’Ingegneria Civile e Ambientale (DICEA) Università di Padova Via Marzolo , 9 - 35131 Padova, Italy
Abstract
AbstractIn sub-Riemannian geometry there exist, in general, no known explicit representations of the heat kernels, and these functions fail to have any symmetry whatsoever. In particular, they are not a function of the control distance, nor they are for instance spherically symmetric in any of the layers of the Lie algebra. Despite these unfavourable aspects, in this paper we establish a new heat semigroup characterisation of the Sobolev and $BV$ spaces in a Carnot group by means of an integral decoupling property of the heat kernel.
Publisher
Oxford University Press (OUP)
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