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

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.

References in corpus (5)

• Hankel Multipliers of Laplace Transform Type
• Square functions in the Hermite setting for functions with values in UMD spaces
• Vector-valued Littewood-Paley-Stein theory for semigroups II
• The fractional Bessel equation in Hölder spaces
• $\gamma$-radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces

Cited by in corpus (1)

• Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions