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Comptes Rendus Mathématique
Volume 355, n° 8
pages 859-865 (août 2017)
Doi : 10.1016/j.crma.2017.07.013
Received : 7 January 2017 ;  accepted : 20 July 2017
Intersection of harmonically weighted Dirichlet spaces
Intersection d'espaces de Dirichlet à poids harmonique
 

Guanlong Bao a , Nihat Gökhan Göğüş b , Stamatis Pouliasis b
a Department of Mathematics, Shantou University, Shantou, Guangdong 515063, China 
b Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul 34956, Turkey 

Abstract

In 1991, S. Richter introduced harmonically weighted Dirichlet spaces  , motivated by his study of cyclic analytic two-isometries. In this paper, we consider  , the intersection of   spaces, where   is the family of Borel probability measures. Several function-theoretic characterizations of the Banach space   are given. We also show that   is located strictly between some classical analytic Lipschitz spaces and   can be regarded as the endpoint case of analytic Morrey spaces in some sense.

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Résumé

En 1991, S. Richter a introduit les espaces de Dirichlet   à poids harmonique, motivé par l'étude des 2-isométries analytiques. Dans cet article, on considère une intersection   d'espaces  , où   est l'espace des mesures de probabilité boréliennes. On donne plusieurs caractérisations de   en termes de théorie des fonctions. On montre également que   se compare dans les deux sens par des relations d'inclusion strictes avec certains espaces de fonctions analytiques Lipschitz et que   peut être considéré comme le cas extrême des espaces de Morrey analytiques en un certain sens.

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