Bad boundary behavior in star invariant subspaces I

Andreas Hartmann (1) , William T. Ross (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Department of Mathematics

We discuss the boundary behavior of functions in backward shift invariant subspaces $(B H^2)^{\perp}$, where $B$ is a Blaschke product. Extending some results of Ahern and Clark, we are particularly interested in the growth rates of functions at points of the spectrum of $B$ where $B$ does not admit a derivative in the sense of Carathéodory.

Mots clés: Hardy spaces; star invariant subspaces; non-tangential limits; Blaschke products

Domaines: Variables complexes [math.CV]

Andreas Hartmann, William T. Ross. Bad boundary behavior in star invariant subspaces I. Arkiv för Matematik, 2014, 52 (1), pp.113-134. ⟨hal-00619239v2⟩