  The two variable Kostka functions are the scalar products of the Macdonald
polynomials with the Schur polynomials with respect to the scalar product which
makes the Hall-Littlewood polynomials pairwise orthogonal. A conjecture of
Macdonald states that they are polynomials in q and t with non-negative
integral coefficients. We prove that the Kostka functions are at least
polynomials with integral coefficients. The main idea is to prove an analogous
statement for the non-symmetric Macdonald polynomials by establishing recursion
relations via the affine Hecke algebra.
