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Revista Matemática Complutense

, Volume 32, Issue 1, pp 57–98 | Cite as

BMO functions and balayage of Carleson measures in the Bessel setting

  • Víctor Almeida
  • Jorge J. Betancor
  • Alejandro J. Castro
  • Juan C. Fariña
  • Lourdes Rodríguez-MesaEmail author
Article
  • 36 Downloads

Abstract

By \(BMO_{\text {o}}(\mathbb {R})\) we denote the space consisting of all those odd and bounded mean oscillation functions on \(\mathbb {R}\). In this paper we characterize the functions in \(BMO_{\text {o}}(\mathbb {R})\) with bounded support as those ones that can be written as a sum of a bounded function on \((0,\infty )\) plus the balayage of a Carleson measure on \((0,\infty )\times (0,\infty )\) with respect to the Poisson semigroup associated with the Bessel operator
$$\begin{aligned} B_\lambda :=-x^{-\lambda }\frac{d}{dx}x^{2\lambda }\frac{d}{dx}x^{-\lambda },\quad \lambda >0. \end{aligned}$$
This result can be seen as an extension to Bessel setting of a classical result due to Carleson.

Keywords

Bessel operators BMO functions Carleson measure Balayage 

Mathematics Subject Classification

30H35 35J15 42B35 42B37 42C05 

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Copyright information

© Universidad Complutense de Madrid 2018

Authors and Affiliations

  1. 1.Departamento de Análisis MatemáticoUniversidad de La LagunaLa LagunaSpain
  2. 2.Department of MathematicsNazarbayev UniversityAstanaKazakhstan

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