  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.
