Sharp fractional Sobolev and related inequalities on H-type groups

Yaojun Wang; Qiaohua Yang

Sharp fractional Sobolev and related inequalities on H-type groups

Analysis of PDEs 2024-06-28 v2

Authors: Yaojun Wang , Qiaohua Yang

Abstract

We determine the sharp constants for the fractional Sobolev inequalities associated with the conformally invariant fractional powers $\mathcal{L}_{s}(0<s<1)$ of the sublaplacian on H-type groups. From these inequalities we derive a sharp log-Sobolev inequality by considering a limiting case and a sharp Sobolev trace inequality. The later extends to this context the result of Frank, Gonz\'alez, Monticelli and Tan (Adv. Math, 2015).

Keywords

fractional Sobolev inequality sharp constants H-type groups log-Sobolev inequality Sobolev trace inequality

Cite

@article{arxiv.2406.16278,
  title  = {Sharp fractional Sobolev and related inequalities on H-type groups},
  author = {Yaojun Wang and Qiaohua Yang},
  journal= {arXiv preprint arXiv:2406.16278},
  year   = {2024}
}

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