Best constants in a class of polymultiplicative inequalities for derivatives

Best constants are found in a class of multiplicative inequalities with k f actors that give an estimate of the C-norm of a function (in R-n or on S-n) in terms of the product of the L-2-norms of fractional powers of the Lapla ce operator. Special attention is given to the detection of the cases of eq uality of the corresponding constants on the sphere and in Euclidean space.