Intersection of harmonically weighted Dirichlet spaces

Guanlong Bao; Nihat Gökhan Göğüş; Stamatis Pouliasis

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

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

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

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

@article{CRMATH_2017__355_8_859_0,
     author = {Guanlong Bao and Nihat G\"okhan G\"o\u{g}\"u\c{s} and Stamatis Pouliasis},
     title = {Intersection of harmonically weighted {Dirichlet} spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {859--865},
     publisher = {Elsevier},
     volume = {355},
     number = {8},
     year = {2017},
     doi = {10.1016/j.crma.2017.07.013},
     language = {en},
}

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Guanlong Bao; Nihat Gökhan Göğüş; Stamatis Pouliasis. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.07.013/

Bibliographie
Cité par

[1] A. Baernstein Analytic functions of bounded mean oscillation (D.A. Brannan; J.G. Clunie, eds.), Aspects of Contemporary Complex Analysis, Academic Press, London, New York, 1980, pp. 3-36

[2] P. Duren Theory of $H^{p}$ Spaces, Academic Press, New York, 1970

[3] O. El-Fallah; K. Kellay; J. Mashreghi; T. Ransford A Primer on the Dirichlet Space, Cambridge Tracts in Mathematics, vol. 203, Cambridge University Press, 2014

[4] G. Hardy; J. Littlewood Some properties of fractional integrals II, Math. Z., Volume 34 (1932), pp. 403-439

[5] E.A. Poletsky Projective limits of Poletsky–Stessin Hardy spaces, Complex Anal. Oper. Theory, Volume 10 (2016) no. 5, pp. 1001-1016

[6] E.A. Poletsky; K.R. Shrestha (Banach Cent. Publ.), Volume vol. 107, Institute of Mathematics of the Polish Academy of Sciences, Warsaw (2015), pp. 195-204

[7] S. Richter A representation theorem for cyclic analytic two-isometries, Trans. Amer. Math. Soc., Volume 328 (1991), pp. 325-349

[8] S. Richter; C. Sundberg A formula for the local Dirichlet integral, Mich. Math. J., Volume 38 (1991), pp. 355-379

[9] S. Richter; C. Sundberg Multipliers and invariant subspaces in the Dirichlet space, J. Oper. Theory, Volume 28 (1992), pp. 167-186

[10] Z. Wu; C. Xie $Q$ spaces and Morrey spaces, J. Funct. Anal., Volume 201 (2003), pp. 282-297

[11] H. Wulan On the coefficients of α-Bloch functions, Math. Montisnigri, Volume 3 (1994), pp. 45-57

[12] J. Xiao Geometric $Q_{p}$ Functions, Birkhäuser Verlag, Basel–Boston–Berlin, 2006

[13] J. Xiao; W. Xu Composition operators between analytic Campanato spaces, J. Geom. Anal., Volume 24 (2014), pp. 649-666

[14] K. Zhu Operator Theory in Function Spaces, American Mathematical Society, Providence, RI, 2007

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