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arXiv · 2406.16278

Sharp fractional Sobolev and related inequalities on H-type groups

Yaojun Wang·Qiaohua Yang
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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).

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Yaojun Wang, Qiaohua Yang. 2024-06-24. Sharp fractional Sobolev and related inequalities on H-type groups. https://arxiv.org/abs/2406.16278

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