Regularity on the boundary in spaces of holomorphic functions on the unit disk

Emmanuel Fricain (1) , Andreas Hartmann (2)

1 ICJ - Institut Camille Jordan
2 IMB - Institut de Mathématiques de Bordeaux

We review some results on regularity on the boundary in spaces of analytic functions on the unit disk connected with backward shift invariant subspaces in $H^p$.

Mots clés: analytic continuation; backward shift; de Branges-Rovnyak spaces; Carleson embedding; invariant subspace; Muckenhoupt condition; one component inner functions; reproducing kernels; rigid functions; spectrum; Toeplitz operators; analytic continuation

Domaines: Variables complexes [math.CV]

Emmanuel Fricain, Andreas Hartmann. Regularity on the boundary in spaces of holomorphic functions on the unit disk. Hilbert spaces of analytic functions, Dec 2008, Montréal, Canada. pp.91-119. ⟨hal-00378875⟩