English

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.

Keywords

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

R2 v1 2026-06-22T01:59:09.113Z