The admissible lower-order coefficients for fractional Sobolev inequalities on the CR sphere are exactly [|S^{2n+1}|^{-s/Q}, ∞) in the linear case and similar threshold sets in the power case, with identical admissible sets on the Heisenberg group.
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Fractional Sobolev-type embedding on CR sphere and Heisenberg group
The admissible lower-order coefficients for fractional Sobolev inequalities on the CR sphere are exactly [|S^{2n+1}|^{-s/Q}, ∞) in the linear case and similar threshold sets in the power case, with identical admissible sets on the Heisenberg group.