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 γ-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.
@article{arxiv.1303.5571,
title = {UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces},
author = {J. J. Betancor and A. J. Castro and L. Rodríguez-Mesa},
journal= {arXiv preprint arXiv:1303.5571},
year = {2023}
}