We study properties of the embedding operators of model sub-spaces K Δp(defined by inner functions) in the Hardy space Hp(coinvariant subspaces of the shift operator). We find acriterion for the embedding of KΔP in Lp(μ) to be compact similar to the Volberg-Treil theorem on bounded embeddings, and give apositive answer to aquestion of Cima and Matheson. The proof is based on Bernstein-type inequalities for functions in KΔP. We investigate measures such that the embedding operator belongs to some Schatten-vonNeumann ideal.

Original languageEnglish
Pages (from-to)1077-1100
Number of pages24
JournalIzvestiya Mathematics
Volume73
Issue number6
DOIs
StatePublished - 1 Dec 2009

    Research areas

  • Carleson measure, Embedding theorem, Hardy space, Inner function

    Scopus subject areas

  • Mathematics(all)

ID: 32722304