Schatten classes of generalized Hilbert operators
Articles
Overview
published in
- Collectanea Mathematica Journal
publication date
- January 2018
start page
- 83
end page
- 105
issue
- 1
volume
- 69
Digital Object Identifier (DOI)
full text
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
Classification
subjects
- Mathematics
keywords
- dirichlet type spaces; schatten classes; generalized hilbert operators; muckenhoupt weight; doubling weights