Intersection of harmonically weighted Dirichlet spaces

Bao, Guanlong; Göğüş, Nihat Gökhan; Pouliasis, Stamatis

doi:10.1016/j.crma.2017.07.013

Mathematical analysis/Complex analysis

Intersection of harmonically weighted Dirichlet spaces
[Intersection d'espaces de Dirichlet à poids harmonique]

Présenté par : the Editorial Board

Bao, Guanlong ¹ ; Göğüş, Nihat Gökhan ² ; Pouliasis, Stamatis ²

¹ Department of Mathematics, Shantou University, Shantou, Guangdong 515063, China
² Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul 34956, Turkey

Comptes Rendus. Mathématique, Tome 355 (2017) no. 8, pp. 859-865.

Résumé
Abstract

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

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

Reçu le : 2017-01-07
Accepté le : 2017-07-20
Publié le : 2017-08-01

DOI : 10.1016/j.crma.2017.07.013

Affiliations des auteurs :

Bao, Guanlong ¹ ; Göğüş, Nihat Gökhan ² ; Pouliasis, Stamatis ²

¹ Department of Mathematics, Shantou University, Shantou, Guangdong 515063, China
² Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istanbul 34956, Turkey

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     title = {Intersection of harmonically weighted {Dirichlet} spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {859--865},
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Bao, Guanlong; Göğüş, Nihat Gökhan; Pouliasis, Stamatis. Intersection of harmonically weighted Dirichlet spaces. Comptes Rendus. Mathématique, Tome 355 (2017) no. 8, pp. 859-865. doi : 10.1016/j.crma.2017.07.013. http://www.numdam.org/articles/10.1016/j.crma.2017.07.013/

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