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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the zeros of functions in Dirichlet-type spaces


Authors: Jordi Pau and José Ángel Peláez
Journal: Trans. Amer. Math. Soc. 363 (2011), 1981-2002
MSC (2000): Primary 30C15, 30D45, 30D50, 30H05
Published electronically: November 18, 2010
MathSciNet review: 2746672
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Abstract: We study the sequences of zeros for functions in the Dirichlet spaces $ \mathcal{D}_s$. Using Carleson-Newman sequences we prove that there are great similarities for this problem in the case $ 0<s<1$ with that for the classical Dirichlet space.


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Additional Information

Jordi Pau
Affiliation: Departament de Matemàtica Aplicada i Analisi, Universitat de Barcelona, 08007 Barcelona, Spain
Email: jordi.pau@ub.edu

José Ángel Peláez
Affiliation: Departament de Análisis Matemático, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain
Email: japelaez@uma.es

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05108-6
PII: S 0002-9947(2010)05108-6
Keywords: Dirichlet spaces, zero sets
Received by editor(s): December 22, 2008
Published electronically: November 18, 2010
Additional Notes: The first author was partially supported by SGR grant $2005$SGR $00774$ and DGICYT grant MTM$2008$-$05561$-$C02$-$01$ (MCyT/MEC), while the second author was supported by: the Ministerio de EduCación y Ciencia, Spain\rq\rq(MTM2007-60854 and MTM2007-30904-E); from \lq\lq La Junta de Andalucía\rq\rq(FQM210 and P06-FQM01504), and by the Ramón y Cajal Program of MICINN (Spain)
Article copyright: © Copyright 2010 American Mathematical Society