  In the paper it is considered the generalized Faber polynomials defined
inside and outside a regular curve on the complex plane. The weighted Smirnov
spaces corresponding to bounded and unbounded regions are defined. It is proved
that the generalized Faber polynomials forms a basis in weighted Smirnov
spaces, if the weight function satisfies the Muckenhoupt condition on the
regular curve. The double system of generalized Faber polynomials with
complex-valued coefficients is also considered and the basis properties of such
a system in weighted Lebesgue spaces over regular curves are studied.
