Best constants in multiplicative inequalities for sup-norms

The paper finds best constants in a class of multiplicative inequalities wi th one-dimensional spatial variables \\f((k))\\(infinity) less than or equal to c(k, l) \\f\\((2l - 2k - 1)\2l)\ \f((l))((2k + 1)/2l) -1/2 < k < l - 1/2 where f is a periodic function with zero mean value, and the norms in the r ight-hand side of the expression are the L-g-norms.