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Sharp fractional Sobolev and related inequalities on H-type groups

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arxiv 2406.16278 v2 pith:2ZBLBS2U submitted 2024-06-24 math.AP

Yaojun Wang , Qiaohua Yang This is my paper · ORCID
classification math.AP
keywords sharpfractionalinequalitiessobolevgroupsh-typeinequalityalez
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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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