Schatten classes of generalized Hilbert operators

• Autores: José Angel Peláez Márquez , Daniel Seco
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 69, Fasc. 1, 2018, págs. 83-105
• Idioma: inglés
• DOI: 10.1007/s13348-017-0195-5
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• Resumen

  • 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−?<∞.