Quasi-equivalence of bases in some Whitney spaces

If the logarithmic dimension of a Cantor-type set K is smaller than 1, then the Whitney space epsilon (K) possesses an interpolating Faber basis. For any generalized Cantor-type set K, a basis in epsilon (K) can be presented by means of functions that are polynomials locally. This gives a plenty of bases in each space epsilon (K). We show that these bases are quasi-equivalent.