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arXiv · 1111.3453

Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions

Jorge J. Betancor·Alejandro J. Castro·Lourdes Rodríguez-Mesa
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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 $\gamma$-radonifying norms. Also we prove that the UMD Banach spaces are the unique Banach spaces for which certain $\gamma$-radonifying Carleson inequalities for Bessel-Poisson integrals of $BMO_o(\mathbb{R},X)$ functions hold.

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Jorge J. Betancor, Alejandro J. Castro, Lourdes Rodríguez-Mesa. 2011-11-15. Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions. https://doi.org/10.1007/s11117-012-0189-1

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