Consider the Schrödinger operator in , where is nonnegative and satisfies the reverse Hölder inequality with exponent (i.e., for every ball ). Let be the semigroup of linear operators generated by , and let . The Hardy space is defined to be . It is shown that can be described in terms of atomic decomposition, much as in the case of the classical real variable , though the notion of an atom is different.
The operators are analogs of the Riesz transforms. It is shown that .