Extremal spaces related to Schr?dinger operators with potentials satisfying a reverse H?lder inequality

摘要

We describe some elements of the theory of semigroups generated by second order differential operators needed to study the Hardy-type space H1 L related to the time independent Schr¨odinger operator L = ?? + V , with V ≥ 0 a potential satisfying a reverse H¨older inequality. Its dual space is a BMO-type space BMOL, that turns out to be the suitable one for the versions of some classical operators associated to L (Hardy-Littlewood, semigroup and Poisson maximal functions, square function, fractional integral operator). We also recall a characterization of BMOL in terms of Carlesson measures.