Intersection of harmonically weighted Dirichlet spaces

Guanlong Bao; Nihat Gökhan Göğüş; Stamatis Pouliasis

doi:10.1016/j.crma.2017.07.013

Intersection of harmonically weighted Dirichlet spaces

Translated title of the contribution: Intersection of harmonically weighted Dirichlet spaces

Guanlong Bao, Nihat Gökhan Göğüş, Stamatis Pouliasis

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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Abstract

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∈PD(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∈PD(μ) are given. We also show that ⋂_μ∈PD(μ) is located strictly between some classical analytic Lipschitz spaces and ⋂_μ∈PD(μ) can be regarded as the endpoint case of analytic Morrey spaces in some sense.

Translated title of the contribution	Intersection of harmonically weighted Dirichlet spaces
Original language	English
Pages (from-to)	859-865
Number of pages	7
Journal	Comptes Rendus Mathematique
Volume	355
Issue number	8
DOIs	https://doi.org/10.1016/j.crma.2017.07.013
State	Published - Aug 2017

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title = "Intersection of harmonically weighted Dirichlet spaces",

abstract = "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∈PD(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∈PD(μ) are given. We also show that ⋂μ∈PD(μ) is located strictly between some classical analytic Lipschitz spaces and ⋂μ∈PD(μ) can be regarded as the endpoint case of analytic Morrey spaces in some sense.",

author = "Guanlong Bao and G{\"o}ğ{\"u}{\c s}, {Nihat G{\"o}khan} and Stamatis Pouliasis",

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AU - Bao, Guanlong

AU - Göğüş, Nihat Gökhan

AU - Pouliasis, Stamatis

PY - 2017/8

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N2 - 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∈PD(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∈PD(μ) are given. We also show that ⋂μ∈PD(μ) is located strictly between some classical analytic Lipschitz spaces and ⋂μ∈PD(μ) can be regarded as the endpoint case of analytic Morrey spaces in some sense.

AB - 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∈PD(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∈PD(μ) are given. We also show that ⋂μ∈PD(μ) is located strictly between some classical analytic Lipschitz spaces and ⋂μ∈PD(μ) can be regarded as the endpoint case of analytic Morrey spaces in some sense.

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JF - Comptes Rendus Mathematique

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ER -

Intersection of harmonically weighted Dirichlet spaces

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