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Improved higher-order Sobolev inequalities on CR sphere (2203.13873v2)
Published 25 Mar 2022 in math.DG
Abstract: We improve higher-order CR Sobolev inequalities on $S{2n+1}$ under the vanishing of higher order moments of the volume element. As an application, we give a new and direct proof of the classification of minimizers of the CR invariant higher-order Sobolev inequalities. In the same spirit, we prove almost sharp Sobolev inequalities for GJMS operators to general CR manifolds, and obtain the existence of minimizers in $C{2k}(N)$ of higher-order CR Yamabe-type problems when $Y_k(N)<Y_k(\mathbb{H}n)$.