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arXiv · 1804.05668

BMO functions and Balayage of Carleson measures in the Bessel setting

Víctor Almeida·Jorge J. Betancor·Alejandro J. Castro·Juan C. Fariña·Lourdes Rodríguez-Mesa
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Abstract

By $BMO_o(R)$ we denote the space consisting of all those odd and bounded mean oscillation functions on R. In this paper we characterize the functions in $BMO_o(R)$ 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 $B_\lambda =-x^{-\lambda }Dx^{2\lambda }Dx^{-\lambda}$, $\lambda >0$. This result can be seen as an extension to Bessel setting of a classical result due to Carleson.

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BibTeXRIS

Víctor Almeida, Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña, Lourdes Rodríguez-Mesa. 2018-04-16. BMO functions and Balayage of Carleson measures in the Bessel setting. https://doi.org/10.1007/s13163-018-0270-9

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