Sobolev spaces on graded groups
Classical Analysis and ODEs
2013-11-04 v1 Spectral Theory
Abstract
We study the Lp-properties of positive Rockland operators and define Sobolev spaces on general graded groups. This generalises the case of sub-Laplacians on stratified groups studied by G. Folland in [3]. We show that the defined Sobolev spaces are actually independent of the choice of a positive Rockland operator. Furthermore, we show that they are interpolation spaces and establish duality and Sobolev embedding theorems in this context.
Cite
@article{arxiv.1311.0192,
title = {Sobolev spaces on graded groups},
author = {Veronique Fischer and Michael Ruzhansky},
journal= {arXiv preprint arXiv:1311.0192},
year = {2013}
}
Comments
41 pages