Abstract. Let

We identify the dual space of the Hardy-type space H 1 L related to the time independent Schrödinger operator L = − + V , with V a potential satisfying a reverse Hölder inequality, as a BMO-type space BMO L . 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 BMO L in terms of Carlesson measures.

In this paper, we study Hardy spaces associated with two Bessel operators. Two different kind of Hardy spaces appear. These differences are transparent in the corresponding atomic decompositions.

Abstract. Let A = −∆ + V be a Schrödinger operator on R d , d ≥ 3, where V is a nonnegative potential satisfying the reverse Hölder inequality with an exponent q > d/2. We say that f is an element ofA admits a special atomic decomposition. Introduction. Let k t (x, y) be the integral kernels of the semigroup of linear operators {T t } t>0 generated by a Schrödinger operatorThroughout this paper we assume that V is a nonnegative potential on R d that belongs to the reverse Hölder class RH q , q > d/2, that is, there exists a constant C > 0 such that