Constrained Nevanlinna-Pick interpolation in Weighted Hardy and Bergman

Given a finite set σ of the unit disc D = {z ∈ C:, |z | < 1} and a holomorphic function f in D which belongs to a class X, we are looking for a function g in another class Y (smaller than X) which minimizes the norm ‖g‖Y among all functions g such that g|σ = f|σ. For Y = H∞, X = lpa(wk) =f =∑ k≥0 f̂(k)zk: ‖f‖p = k≥