  A systematic study of the representation theory of double affine Hecke
algebras and related harmonic analysis is started in this paper. Continuing the
previous papers we use the technique of intertwining operators to create
Macdonald polynomials, estimate their denominators, generalize the classical
representations of p-adic affine Hecke algebras in the spaces of functions on
affine Weyl groups, and to find out when induced representations are
irreducible and co-spherical. The connection with recent results by Sahi and
Knop on the integrality of the Macdonald polynomials is established.
