Year: 2026
Type: preprint
Abstract: In this paper we establish improved Sobolev inequalities on the quaternionic sphere under higher-order moment vanishing conditions with respect to the measure \(|u|^{p^*}\,dξ\). As an application, we give a new proof of the existence of extremals for the sharp Sobolev embedding \[ S^{1,2}(S^{4n+3}) \hookrightarrow L^{2^*}(S^{4n+3}). \]
Source: arXiv (Cornell University)
Authors: Ren, Zongxiong, Yang, Zhipeng
Institution: Yunnan Normal University
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G6285904573
OpenAlex ID: W7147496948
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