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Concrete Operators

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Mathematical Citation Quotient (MCQ) 2017: 0.34

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Some Hilbert spaces related with the Dirichlet space

Nicola Arcozzi / Pavel Mozolyako
  • Chebyshev Lab at St. Petersburg State University, 14th Line 29B, Vasilyevsky Island, St. Petersburg 199178, Russia
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/ Karl-Mikael Perfekt
  • Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
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/ Stefan Richter / Giulia Sarfatti
  • Istituto Nazionale di Alta Matematica “F. Severi”, Città Universitaria, Piazzale Aldo Moro 5, 00185 Roma, and Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4, place Jussieu, F-75252 Paris, France
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Published Online: 2016-06-28 | DOI: https://doi.org/10.1515/conop-2016-0011

Abstract

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.

Keywords: Dirichlet space; Complete Nevanlinna Property; Hilbert-Schmidt operators; Carleson measures

References

  • [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. Google Scholar

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

  • [4] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68, (1950) 337-404. 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). 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. 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. 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. Google Scholar

About the article

Received: 2015-12-23

Accepted: 2015-05-16

Published Online: 2016-06-28


Citation Information: Concrete Operators, Volume 3, Issue 1, Pages 94–101, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2016-0011.

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© 2016 Arcozzi et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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