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arXiv · 1311.0192

Sobolev spaces on graded groups

Veronique Fischer·Michael Ruzhansky
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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.

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Veronique Fischer, Michael Ruzhansky. 2013-11-01. Sobolev spaces on graded groups. https://arxiv.org/abs/1311.0192

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