Schatten classes of generalized Hilbert operators

2015/10/19 by Peláez, José Ángel, Seco, Daniel · 1 citation
#47G10 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 47B10 Secondary: 31C25

paper · doi:10.48550/arxiv.1510.05455

Abstract

Let D_v denote the Dirichlet type space in the unit disc induced by a radial weight v for which \widehatv(r)=∫_r¹ v(s) ds satisfies the doubling property ∫_r¹ v(s) ds≤ C ∫_(1+r)/(2)¹ v(s) ds. In this paper, we characterize the Schatten classes S_p(D_v) of the generalized Hilbert operators H_g(f)(z)=∫₀¹f(t)g'(tz) dt acting on D_v, where v satisfies the Muckenhoupt-type conditions sup_0

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• Duality of mixed norm spaces induced by radial one-sided doubling weight

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