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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access June 28, 2016

Some Hilbert spaces related with the Dirichlet space

  • Nicola Arcozzi , Pavel Mozolyako , Karl-Mikael Perfekt , Stefan Richter and Giulia Sarfatti
From the journal Concrete Operators


We study the reproducing kernel Hilbert space with kernel kd , where d is a positive integer and k is the reproducing kernel of the analytic Dirichlet space.


[1] J. Agler, J. E. McCarthy, Pick interpolation and Hilbert function spaces, Graduate Studies in Mathematics, 44 (American Mathematical Society, Providence, RI, 2002), xx+308 pp. ISBN: 0-8218-2898-3. 10.1090/gsm/044Search in Google Scholar

[2] N. Arcozzi, R. Rochberg, E. Sawyer, Carleson measures for analytic Besov spaces, Rev. Mat. Iberoamericana 18 (2002), no. 2, 443-510. Search in Google Scholar

[3] N. Arcozzi, R. Rochberg, E. Sawyer, B. D. Wick, Function spaces related to the Dirichlet space, J. Lond. Math. Soc. (2) 83 (2011), no. 1, 1-18. Search in Google Scholar

[4] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68, (1950) 337-404. 10.1090/S0002-9947-1950-0051437-7Search in Google Scholar

[5] D. Bekollé, A. Bonami, Inégalités à poids pour le noyau de Bergman, C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 18, A775- A778 (in French). Search in Google Scholar

[6] B. Boe, An interpolation theorem for Hilbert spaces with Nevanlinna-Pick kernel, Proc. Amer. Math. Soc. 133 (2005), no. 7, 2077- 2081. Search in Google Scholar

[7] D. H. Luecking, Representation and duality in weighted spaces of analytic functions, Indiana Univ. Math. J. 34 (1985), no. 2, 319- 336. Search in Google Scholar

[8] K. Seip, Interpolation and sampling in spaces of analytic functions, University Lecture Series, 33 (American Mathematical Society, Providence, RI, 2004), xii+139 pp. ISBN: 0-8218-3554-8. Search in Google Scholar

Received: 2015-12-23
Accepted: 2015-5-16
Published Online: 2016-6-28

© 2016 Arcozzi et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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