Some Hilbert spaces related with the Dirichlet space

Nicola Arcozzi; Pavel Mozolyako; Karl-Mikael Perfekt; Stefan Richter; Giulia Sarfatti

Concrete Operators (2016)

  • Volume: 3, Issue: 1, page 94-101
  • ISSN: 2299-3282

Abstract

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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.

How to cite

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Nicola Arcozzi, et al. "Some Hilbert spaces related with the Dirichlet space." Concrete Operators 3.1 (2016): 94-101. <http://eudml.org/doc/281190>.

@article{NicolaArcozzi2016,
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.},
author = {Nicola Arcozzi, Pavel Mozolyako, Karl-Mikael Perfekt, Stefan Richter, Giulia Sarfatti},
journal = {Concrete Operators},
keywords = {Dirichlet space; Complete Nevanlinna Property; Hilbert-Schmidt operators; Carleson measures; complete Nevanlinna property},
language = {eng},
number = {1},
pages = {94-101},
title = {Some Hilbert spaces related with the Dirichlet space},
url = {http://eudml.org/doc/281190},
volume = {3},
year = {2016},
}

TY - JOUR
AU - Nicola Arcozzi
AU - Pavel Mozolyako
AU - Karl-Mikael Perfekt
AU - Stefan Richter
AU - Giulia Sarfatti
TI - Some Hilbert spaces related with the Dirichlet space
JO - Concrete Operators
PY - 2016
VL - 3
IS - 1
SP - 94
EP - 101
AB - 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.
LA - eng
KW - Dirichlet space; Complete Nevanlinna Property; Hilbert-Schmidt operators; Carleson measures; complete Nevanlinna property
UR - http://eudml.org/doc/281190
ER -

References

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  1. [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.  Zbl1010.47001
  2. [2] N. Arcozzi, R. Rochberg, E. Sawyer, Carleson measures for analytic Besov spaces, Rev. Mat. Iberoamericana 18 (2002), no. 2, 443-510.  Zbl1059.30051
  3. [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.  Zbl1232.30036
  4. [4] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68, (1950) 337-404.  Zbl0037.20701
  5. [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).  Zbl0398.30006
  6. [6] B. Boe, An interpolation theorem for Hilbert spaces with Nevanlinna-Pick kernel, Proc. Amer. Math. Soc. 133 (2005), no. 7, 2077- 2081.  Zbl1065.30053
  7. [7] D. H. Luecking, Representation and duality in weighted spaces of analytic functions, Indiana Univ. Math. J. 34 (1985), no. 2, 319- 336.  Zbl0538.32004
  8. [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.  

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