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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Carleson measures on Dirichlet-type spaces


Author: Gerardo R. Chacón
Journal: Proc. Amer. Math. Soc. 139 (2011), 1605-1615
MSC (2000): Primary 42B25; Secondary 46C99, 31C25
Published electronically: January 11, 2011
MathSciNet review: 2763750
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Abstract: We show that a maximal inequality holds for the non-tangential maximal operator on Dirichlet spaces with harmonic weights on the open unit disc. We then investigate two notions of Carleson measures on these spaces and use the maximal inequality to give characterizations of the Carleson measures in terms of an associated capacity.


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Additional Information

Gerardo R. Chacón
Affiliation: Departamento de Matemáticas, Pontificia Universidad Javeriana, Bogotá, Colombia
Email: chacong@javeriana.edu.co

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10823-2
PII: S 0002-9939(2011)10823-2
Keywords: Dirichlet-type spaces, non-tangential maximal function, maximal inequality, Carleson measures
Received by editor(s): April 26, 2010
Published electronically: January 11, 2011
Communicated by: Richard Rochberg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.