Schatten classes of generalized Hilbert operators Articles uri icon

publication date

  • January 2018

start page

  • 83

end page

  • 105

issue

  • 1

volume

  • 69

International Standard Serial Number (ISSN)

  • 0010-0757

abstract

  • Let Dv denote the Dirichlet type space in the unit disc induced by a radial weight v for which vˆ(r)=∫1rv(s)ds satisfies the doubling property ∫1rv(s)ds≤C∫11+r2v(s)ds. In this paper, we characterize the Schatten classes Sp(Dv) of the generalized Hilbert operators Hg(f)(z)=∫10f(t)g′(tz)dtacting on Dv, where v satisfies certain Muckenhoupt type conditions. For p≥1, it is proved that Hg∈Sp(Dv) if and only if ∫10((1−r)∫pi−pi|g′(reitheta)|2dtheta)p2dr1−r

keywords

  • dirichlet type spaces; schatten classes; generalized hilbert operators; muckenhoupt weight; doubling weights