We prove multiplicative interpolation inequalities for the imbeddings of the Sobolev space H1(S2) into Lq for q ∈ [1,∞). The case of zero-mean functions is considered and similar inequalities for tangent vector functions. The corresponding constants are explicitly found with sharp rate of growth with respect to q as q → ∞. In the one-dimensional periodic case the corresponding inequalities are proved in the critical case H 1/2 (S1) →Lq(S1) for all q ∈ [1,∞).
