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本文在球面SN上建立了一类最佳Sobolev不等式:‖f‖2Lq(SN)≤(q-2)Γ(N-d)2+1/dΓ(N+d/2))(∫SNf(ξ)Adf(ξ)dξ-Γ(N+d/2)Γ/(N-d/2)∫SN |f丨2dξ)+∫SN丨f丨2dξ,其中Ad(0＜d＜N)是SN上的高阶保形算子,dξ是SN的归一化曲面测度,2≤q＜2N/N-d.“,”This paper is devoted to establishing a class of sharp Sobolev inequalities on the sphere SN,which have the form‖f‖2Lq(SN)≤(q-2)Γ(N-d/2+1/dΓ(N+d/2))(∫SNf(ξ)Adf(ξ)dξ-Γ(N+d/2)/Γ(N-d/2))∫SN丨f丨2dξ)+∫SN丨f丨2dξ where Ad(0＜d＜N)is the higher conformal operator,dξ is the normalized surface measure on SN and 2≤q＜2N/n-d.