Publication:
Schatten classes of generalized Hilbert operators

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2018-01
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Springer
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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)dt acting 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)∫π−π|g′(reiθ)|2dθ)p2dr1−r<∞.
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Dirichlet type spaces, Schatten classes, Generalized hilbert operators, Muckenhoupt weight, Doubling weights
Bibliographic citation
Peláez, J. N. & Seco, D. (2017). Schatten classes of generalized Hilbert operators. Collectanea Mathematica, 69(1), pp. 83–105.