Hardy Approximation to L ^p Functions on Subsets of the Circle with 1< =p< = infinity

Abstract.

We consider approximation of L ^p functions by Hardy functions on subsets of the circle for $1 \leq p < \infty$ . After some preliminaries on the possibility of such an approximation which are connected to recovery problems of the Carleman type, we prove existence and uniqueness of the solution to a generalized extremal problem involving norm constraints on the complementary subset.