Maximal operators, Riesz transforms and Littlewood–Paley functions associated with Bessel operators on BMO

In this paper we study boundedness properties of certain harmonic analysis operators (maximal operators for heat and Poisson semigroups, Riesz transforms and Littlewood–Paley g-functions) associated with Bessel operators, on the space BMOo(R) that consists of the odd functions with bounded mean oscillation on R.