<i>H</i> ^∞ interpolation constrained by Beurling–Sobolev norms

Abstract We consider a Nevanlinna–Pick interpolation problem on finite sequences of the unit disc, constrained by Beurling–Sobolev norms. find sharp asymptotics corresponding quantities, thereby improving known estimates. On our way we obtain S. M. Nikolskii type inequality for rational functions whose poles lie outside disc. It shows that embedding Hardy space H 2 into Wiener algebra absolutely convergent Fourier/Taylor series is invertible subset given degree, remain at distance from circle.