Estimates in corona theorems for some subalgebras of H∞

If n is a non-negative integer, then denote by delta H--n(infinity) the space of all complexvalued functions f defined on B such that f, f((1)), f((2)),..., f ((n)) belong to H-infinity, with the norm [GRAPHICS] We prove bounds on the solution in the corona problem for delta H--n(infinity). As corollaries, we obtain estimates in the corona theorem also for some other subalgebras of the Hardy space H-infinity.