Abstract: The best constants of Sobolev embeddings of four
subspaces of into are
obtained. Also, it is clarified that the expression of the best constants and
the functions achieving them depend remarkably on the inner product assumed for
each of these subspaces. Moreover, we obtain the best constants for some
Kolmogorov type inequalities.
Keywords and phrases: Sobolev inequality, Kolmogorov type inequality, best constant.
