Extremal functions and approximate inversion formulas for weighted Hardy spaces

Abstract

In this paper we consider the weighted Hardy space H_β. This space which gives a generalization of some Hilbert spaces of analytic functions on the unit disk like, the Hardy space H , the weighted Bergman space B_ν and the weighted Dirichlet space D_ν, it plays a background to our contribution. Especially, we examine the extremal functions for the primitive operator Pf(z) := R [0,z] f(w)dw, where [0, z] = {tz, t ∈ [0, 1]}; and we deduce approximate inversion formulas for the operator P on the weighted Hardy space H_β.