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Weak type (1,1) estimates for Caffarelli-Calderón generalized maximal operators for semigroups associated with Bessel and Laguerre operators


Authors: J. J. Betancor, A. J. Castro, P. L. De Nápoli, J. C. Fariña and L. Rodríguez-Mesa
Journal: Proc. Amer. Math. Soc. 142 (2014), 251-261
MSC (2010): Primary 42B25; Secondary 44A15, 43A15
DOI: https://doi.org/10.1090/S0002-9939-2013-11950-7
Published electronically: October 1, 2013
MathSciNet review: 3119200
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Abstract: In this paper we prove that the generalized (in the sense of Caffarelli and Calderón) maximal operators associated with heat semigroups for Bessel and Laguerre operators are weak type $ (1,1)$. Our results include other known ones, and our proofs are simpler than the ones for the known special cases.


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Additional Information

J. J. Betancor
Affiliation: Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, s/n, 38271, La Laguna (Sta. Cruz de Tenerife), Spain
Email: jbetanco@ull.es

A. J. Castro
Affiliation: Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, s/n, 38271, La Laguna (Sta. Cruz de Tenerife), Spain
Email: ajcastro@ull.es

P. L. De Nápoli
Affiliation: Departamento de Matemática, Universidad de Buenos Aires, e Instituto de Investigaciones Matemáticas, “Luis A. Santaló”, CONICET 1248 Pabellón 1, Ciudad Universitaria, Buenos Aires, Argentina
Email: pdenapo@dm.uba.ar

J. C. Fariña
Affiliation: Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, s/n, 38271, La Laguna (Sta. Cruz de Tenerife), Spain
Email: jcfarina@ull.es

L. Rodríguez-Mesa
Affiliation: Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, s/n, 38271, La Laguna (Sta. Cruz de Tenerife), Spain
Email: lrguez@ull.es

DOI: https://doi.org/10.1090/S0002-9939-2013-11950-7
Keywords: Maximal operators, Bessel, Laguerre, heat semigroups of operators
Received by editor(s): March 7, 2012
Published electronically: October 1, 2013
Additional Notes: The authors were partially supported by MTM2010/17974
The second author was also supported by an FPU grant from the government of Spain
The third author was also partially supported by CONICET (Argentina) under PIP 1420090100230, by ANPCYT under PICT 01307, and by UBACyT research project 20020090 100067
Dedicated: Dedicated to the memory of our friend Professor Pablo González Vera
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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