Weak compactness and essential norms of integration operators

Jussi Laitila; Santeri Miihkinen; Pekka J. Nieminen

Weak compactness and essential norms of integration operators

Functional Analysis 2011-01-25 v1 Complex Variables

Authors: Jussi Laitila , Santeri Miihkinen , Pekka J. Nieminen

Abstract

Let $g$ be an analytic function on the unit disc and consider the integration operator of the form $T_g f(z) = \int_0^z fg'\,d\zeta$ . We show that on the spaces $H^1$ and $BMOA$ the operator $T_g$ is weakly compact if and only if it is compact. In the case of $BMOA$ this answers a question of Siskakis and Zhao. More generally, we estimate the essential and weak essential norms of $T_g$ on $H^p$ and $BMOA$ .

Keywords

weak convergence bergman spaces univalent functions

Cite

@article{arxiv.1101.4329,
  title  = {Weak compactness and essential norms of integration operators},
  author = {Jussi Laitila and Santeri Miihkinen and Pekka J. Nieminen},
  journal= {arXiv preprint arXiv:1101.4329},
  year   = {2011}
}

Related papers

View all related →

Complex Variables · Mathematics

Essential norms and weak compactness of integral operators between weighted Bergman spaces