Abstract
In this paper we consider the space \({{{BMO}_o(\mathbb{R}, X)}}\) of bounded mean oscillations and odd functions on \({{\mathbb{R}}}\) taking values in a UMD Banach space X. The functions in \({{{BMO}_o(\mathbb{R}, X)}}\) are characterized by Carleson type conditions involving Bessel convolutions and γ-radonifying norms. Also we prove that the UMD Banach spaces are the unique Banach spaces for which certain γ-radonifying Carleson inequalities for Bessel–Poisson integrals of \({{{BMO}_o(\mathbb{R}, X)}}\) functions hold.
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The authors are partially supported by MTM2010/17974. A. J. Castro is also supported by a FPU grant from the Government of Spain.
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Betancor, J.J., Castro, A.J. & Rodríguez-Mesa, L. Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions. Positivity 17, 535–587 (2013). https://doi.org/10.1007/s11117-012-0189-1
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DOI: https://doi.org/10.1007/s11117-012-0189-1