Mathematical analysis/Complex analysis
Intersection of harmonically weighted Dirichlet spaces
Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 859-865.

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 μPD(μ), the intersection of D(μ) spaces, where P is the family of Borel probability measures. Several function-theoretic characterizations of the Banach space μPD(μ) are given. We also show that μPD(μ) is located strictly between some classical analytic Lipschitz spaces and μPD(μ) can be regarded as the endpoint case of analytic Morrey spaces in some sense.

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 μPD(μ) d'espaces D(μ), où P est l'espace des mesures de probabilité boréliennes. On donne plusieurs caractérisations de μPD(μ) en termes de théorie des fonctions. On montre également que μPD(μ) se compare dans les deux sens par des relations d'inclusion strictes avec certains espaces de fonctions analytiques Lipschitz et que μPD(μ) peut être considéré comme le cas extrême des espaces de Morrey analytiques en un certain sens.

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DOI: 10.1016/j.crma.2017.07.013
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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Bao, Guanlong; Göğüş, Nihat Gökhan; Pouliasis, Stamatis. Intersection of harmonically weighted Dirichlet spaces. Comptes Rendus. Mathématique, Volume 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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