BOURGAIN ALGEBRAS ON THE MAXIMAL IDEAL SPACE OF H-INFINITY

Let B be a Douglas algebra. For another Douglas algebra D, by considering the integral representation, there exists the corresponding closed subspace ($) over cap D of C(M(B)) the space of continuous functions on maximal ideal space of B. Let [($) over cap D](M(B)) be the closed subalgebra of C(M(B)) generated by ($) over cap D. In this paper we describe the algebra [($) over cap D](M(B)) and determine the Bourgain algebra of [($) over cap D](M(B)) relative to C(M(B)).