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Harmonic analysis operators associated with multidimensional Bessel operators

Published online by Cambridge University Press:  20 September 2012

Jorge J. Betancor ,
Alejandro J. Castro  and
Jezabel Curbelo
Jorge J. Betancor
Affiliation:
Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avenida Astrofísico Francisco Sánchez, s/n 38271 La Laguna (Sta. Cruz de Tenerife), Spain (jbetanco@ull.es; ajcastro@ull.es)
Alejandro J. Castro
Affiliation:
Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avenida Astrofísico Francisco Sánchez, s/n 38271 La Laguna (Sta. Cruz de Tenerife), Spain (jbetanco@ull.es; ajcastro@ull.es)
Jezabel Curbelo
Affiliation:
Instituto de Ciencias Matemáticas (CSIC, UAM, UC3M, UCM), Consejo Superior de Investigaciones Científicas, Calle Nicolás Cabrera 15, 28049 Madrid, Spain (jezabel.curbelo@icmat.es)
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Abstract

We establish that the maximal operator and the Littlewood–Paley g-function associated with the heat semigroup defined by multidimensional Bessel operators are of weak type (1, 1). We also prove that Riesz transforms in the multidimensional Bessel setting are of strong type (p, p), for every 1 < p < ∞, and of weak type (1, 1).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 5 , October 2012 , pp. 945 - 974
Copyright
Copyright © Royal Society of Edinburgh 2012

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