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Exponential self-improvement of generalized Poincaré inequalities associated with approximations of the identity and semigroups


Author: Ana Jiménez-del-Toro
Journal: Trans. Amer. Math. Soc. 364 (2012), 637-660
MSC (2000): Primary 46E35; Secondary 47D06, 46E30, 42B25
DOI: https://doi.org/10.1090/S0002-9947-2011-05344-4
Published electronically: September 14, 2011
MathSciNet review: 2846346
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Abstract: The purpose of this paper is to present a general method that allows us to study exponential self-improving properties of generalized Poincaré inequalities associated with an approximation of the identity or a semigroup. In particular, we show the connection between our results and the John-Nirenberg theorem for the space $ BMO$ associated with approximations of the identity and semigroups.


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Additional Information

Ana Jiménez-del-Toro
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049 Madrid, Spain
Email: anajimtor@hotmail.com

DOI: https://doi.org/10.1090/S0002-9947-2011-05344-4
Keywords: Semigroups, BMO, Poincaré inequalities, heat kernels, self-improving properties, weights, space of homogeneous type
Received by editor(s): March 13, 2009
Received by editor(s) in revised form: July 16, 2009
Published electronically: September 14, 2011
Additional Notes: This research was supported by MEC Grant MTM2007-60952 and by UAM-CM Grant CCG07-UAM/ESP-1664.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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