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UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces

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arxiv 1303.5571 v1 pith:BZL2ZS65 submitted 2013-03-22 math.CA math.FA

J.J. Betancor , A.J. Castro , L. Rodríguez-Mesa This is my paper
classification math.CAmath.FA
keywords hardyspacesassociatedbanachbesselfunctionsoperatorssquare
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abstract

We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square functions associated with Poisson semigroups for Bessel operators are defined by using fractional derivatives. If B is a UMD Banach space we obtain for B-valued Hardy and BMO spaces equivalent norms involving $\gamma$-radonifying operators and square functions. We also establish characterizations of UMD Banach spaces by using Hardy and BMO-boundedness properties of g-functions associated to Bessel-Poisson semigroup.

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