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arXiv · 1303.5571

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

J. J. Betancor·A. J. Castro·L. Rodríguez-Mesa
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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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J. J. Betancor, A. J. Castro, L. Rodríguez-Mesa. 2013-03-22. UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces. https://doi.org/10.1007/s00020-014-2202-5

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