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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Carleson measures and reproducing kernel thesis in Dirichlet-type spaces


Authors: G. R. Chacón, E. Fricain and M. Shabankhah
Original publication: Algebra i Analiz, tom 24 (2012), nomer 6.
Journal: St. Petersburg Math. J. 24 (2013), 847-861
MSC (2010): Primary 46E20, 46E22
Published electronically: September 23, 2013
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Abstract: In the paper, a generalization of a Richter and Sundberg representation theorem is employed to obtain a new characterization of Carleson measures for the Dirichlet-type space $ \mathcal {D}(\mu )$ when $ \mu $ is a finite sum of point masses. A reproducing kernel thesis result is also established in this case.


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Additional Information

G. R. Chacón
Affiliation: Departamento de Matematicas, Pontificia Universidad Javeriana, Cra. 7 No. 43-82, Bogotá, Colombia
Email: chacong@javeriana.edu.co

E. Fricain
Affiliation: Laboratoire Paul Painlevé, UMR 8524, Université Lille 1, 59655 Villeneuve d’Ascq Cedex, France
Email: emmanuel.fricain@math.univ-lille1.fr

M. Shabankhah
Affiliation: Department of Engineering Science, College of Engineering, University of Tehran, Tehran 11155-4563, Iran
Email: mahmood.shabankhan@gmail.com

DOI: http://dx.doi.org/10.1090/S1061-0022-2013-01269-6
PII: S 1061-0022(2013)01269-6
Keywords: Dirichlet-type spaces, Carleson measures, reproducing kernel thesis
Received by editor(s): February 16, 2012
Published electronically: September 23, 2013
Additional Notes: The first author was partially supported by Pontifica Universidad Javeriana, project 4884. The second author was partially supported by the ANR FRAB. The third author was supported by ANR DYNOP and FQRNT
Article copyright: © Copyright 2013 American Mathematical Society