Schatten classes of generalized Hilbert operators
- José Angel Peláez Márquez
- Daniel Seco
ISSN: 0010-0757
Argitalpen urtea: 2018
Alea: 69
Faszikulua: 1
Orrialdeak: 83-105
Mota: Artikulua
Beste argitalpen batzuk: Collectanea mathematica
Laburpena
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−�<∞.
Finantzaketari buruzko informazioa
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.Finantzatzaile
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Seventh Framework Programme
European Union
- FP/2007-2013
-
European Research Council
European Union
- 291497
-
Ministerio de Economía y Competitividad
Spain
- MTM2015-69323-REDT
-
Junta de Andalucía
Spain
- P09-FQM-4468