Schatten classes of generalized Hilbert operators

  1. José Angel Peláez Márquez
  2. Daniel Seco
Revista:
Collectanea mathematica

ISSN: 0010-0757

Año de publicación: 2018

Volumen: 69

Fascículo: 1

Páginas: 83-105

Tipo: Artículo

DOI: 10.1007/S13348-017-0195-5 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Collectanea mathematica

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−�<∞.

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Información de financiación

The research leading to these results has received partial funding from Ministerio de Economía y Competitividad, Spain, Projects MTM2011-24606, MTM2014-52865-P and MTM2015-69323-REDT; from La Junta de Andalucía, (FQM210) and (P09-FQM-4468); and from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement No. 291497.

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Fuente de los datos: Dialnet