Harmonic analysis operators associated with multidimensional Bessel operators

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...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2012-10, Vol.142 (5), p.945-974
Main Authors: Betancor, Jorge J., Castro, Alejandro J., Curbelo, Jezabel
Format: Article
Language:English
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Summary: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).
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210511000643