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Resumen de Schatten classes of generalized Hilbert operators

José Angel Peláez Márquez Árbol académico, Daniel Seco

  • Let ? denote the Dirichlet type space in the unit disc induced by a radial weight v for which ?ˆ(?)=∫1??(?)d? satisfies the doubling property ∫1??(?)d?≤?∫11+?2?(?)d?. In this paper, we characterize the Schatten classes ??(?) of the generalized Hilbert operators ?(?)(?)=∫10?(?)?′(??)d? acting on ? , where v satisfies certain Muckenhoupt type conditions. For ?≥1 , it is proved that ?∈??(?) if and only if ∫10((1−?)∫?−?|?′(?e??)|2d?)?2d?1−?<∞.

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