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

Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

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

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Basel AG
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-012-0189-1
Publisher site
See Article on Publisher Site

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.

Journal

PositivitySpringer Journals

Published: Jun 26, 2012

References

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