BMO spaces related to Schrödinger operators with potentials satisfying a reverse Hölder inequality ∗

We identify the dual space of the Hardy-type space H1L related to the time independent Schrödinger operator L = −∆+ V, with V a potential satisfying a reverse Hölder inequality, as a BMO-type space BMOL. We prove the boundedness in this space of the versions of some classical operators associated to L (Hardy-Littlewood, semigroup and Poisson maximal functions, square function, fractional integral operator). We also get a characterization of BMOL in terms of Carlesson measures.