Qp spaces and Dirichlet type spaces

Guanlong Bao, Nihat Gökhan Gögüş, Stamatis Pouliasis

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In this paper, we show that the Möbius invariant function space Qp can be generated by variant Dirichlet type spaces Dμ, p induced by finite positive Borei measures j on the open unit disk. A criterion for the equality between the space p and the usual Dirichlet type space Dμ, p is given. We obtain a sufficient condition to construct different Dμ, p spaces and provide examples. We establish decomposition theorems for Dμ, p spaces and prove that the non-Hilbert space Qp is equal to the intersection of Hilbert spaces Dμ, p. As an application of the relation between Qp and Dμ, p spaces, we also obtain that there exist different Dμ, p spaces; this is a trick to prove the existence without constructing examples.

Original languageEnglish
Pages (from-to)690-704
Number of pages15
JournalCanadian Mathematical Bulletin
Volume60
Issue number4
DOIs
StatePublished - Dec 2017

Keywords

  • Dirichlet type space
  • Möbius invariant function space
  • Qp space

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