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Riesz transform and g-function associated with Bessel operators and their appropriate Banach spaces

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Abstract

We study g-functions and Riesz transforms related to the Bessel operators

$$ \Delta _\mu = - x^{\_\mu \_1/2} Dx^{2\mu + 1} Dx^{\_\mu \_1/2} . $$

The method we use allows us to characterize the Banach spaces \( \mathbb{B} \) for which these operators are bounded when acting on \( \mathbb{B} \)-valued functions.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de La Laguna, 38271-La Laguna., Tenerife, Islas Canarias, Spain

    Jorge J. Betancor & Juan Carlos Fariña

  2. Departamento de Matemáticas, Universidad Autónoma de Madrid Ciudad, Universitaria de Canto Blanco, 28049, Madrid, Spain

    Teresa Martínez & José Luis Torrea

Authors
  1. Jorge J. Betancor
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  2. Juan Carlos Fariña
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  3. Teresa Martínez
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  4. José Luis Torrea
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Additional information

First and second authors were partially supported by Consejería de Educación, Gobierno de Canarias PI2003/068 and DGI grant MTM2004-05878.

Third and fourth authors were partially supported by BFM grant 2002-04013-C02-02.

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Betancor, J.J., Fariña, J.C., Martínez, T. et al. Riesz transform and g-function associated with Bessel operators and their appropriate Banach spaces. Isr. J. Math. 157, 259–282 (2007). https://doi.org/10.1007/s11856-006-0011-5

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  • DOI: https://doi.org/10.1007/s11856-006-0011-5

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