Abstract
We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood–Paley–Stein square functions, multipliers of Laplace transform type and Riesz transforms. We show that these are (vector-valued) Calderón–Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory.
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Communicated by K. Gröchenig.
J. J. Betancor was partially supported by MTM2007/65609. A. J. Castro was supported by a grant for Master studies of “la Caixa”. A. Nowak was partially supported by MNiSW Grant N N201 417839.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Betancor, J.J., Castro, A.J. & Nowak, A. Calderón–Zygmund operators in the Bessel setting. Monatsh Math 167, 375–403 (2012). https://doi.org/10.1007/s00605-011-0348-7
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DOI: https://doi.org/10.1007/s00605-011-0348-7
Keywords
- Bessel operator
- Bessel semigroup
- Maximal operator
- Square function
- Multiplier
- Riesz transform
- Calderón–Zygmund operator