Schatten classes of integration operators on Dirichlet spaces

Jordi Pau; José Ángel Peláez

Schatten classes of integration operators on Dirichlet spaces

Functional Analysis 2013-02-12 v1 Complex Variables

Authors: Jordi Pau , José Ángel Peláez

Abstract

We address the question of describing the membership to Schatten-Von Neumann ideals $\mathcal{S}_ p$ of integration operators $(T_ g f)(z)=\int_{0}^{z}f(\zeta)\,g'(\zeta)\,d\zeta$ acting on Dirichlet type spaces. We also study this problem for multiplication, Hankel and Toeplitz operators. In particular, we provide an extension of Luecking's result on Toeplitz operators.

Keywords

toeplitz operators

Cite

@article{arxiv.1302.2417,
  title  = {Schatten classes of integration operators on Dirichlet spaces},
  author = {Jordi Pau and José Ángel Peláez},
  journal= {arXiv preprint arXiv:1302.2417},
  year   = {2013}
}

Comments

Accepted for publication in Journal d' Analyse Mathem\'atique, (2012)

Related papers

View all related →