Some Hilbert spaces related with the Dirichlet space

• Autorzy: Nicola Arcozzi , Pavel Mozolyako , Karl-Mikael Perfekt , Stefan Richter , Giulia Sarfatti
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2016
• Tom: 3
• Numer: 1
• Strony: 94-101

Daty

zaakceptowano

2015-05-16

otrzymano

2015-12-23

online

2016-06-28

Twórcy

autor

Nicola Arcozzi

• Università di Bologna, Dipartimento di Matematica, Piazza di Porta S.Donato 5, Bologna

autor

Pavel Mozolyako

• Chebyshev Lab at St. Petersburg State University, 14th Line 29B, Vasilyevsky Island, St. Petersburg 199178, Russia

autor

Karl-Mikael Perfekt

• Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway

autor

Stefan Richter

• Department of Mathematics, The University of Tennessee, Knoxville, TN 37996, USA

autor

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

Bibliografia

• [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.
• [2] N. Arcozzi, R. Rochberg, E. Sawyer, Carleson measures for analytic Besov spaces, Rev. Mat. Iberoamericana 18 (2002), no. 2, 443-510.
• [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.
• [4] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68, (1950) 337-404.
• [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).
• [6] B. Boe, An interpolation theorem for Hilbert spaces with Nevanlinna-Pick kernel, Proc. Amer. Math. Soc. 133 (2005), no. 7, 2077- 2081.
• [7] D. H. Luecking, Representation and duality in weighted spaces of analytic functions, Indiana Univ. Math. J. 34 (1985), no. 2, 319- 336.
• [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.

Identyfikatory

DOI

10.1515/conop-2016-0011