ISOMORPHISMS AND SEVERAL CHARACTERIZATIONS OF MUSIELAK-ORLICZ-HARDY SPACES ASSOCIATED WITH SOME SCHRODINGER OPERATORS

Let L a parts per thousand" -Delta + V be a Schrodinger operator on a"e (n) with n a (c) 3/4 3 and V a (c) 3/4 0 satisfying Delta(-1) V a L (a)(a"e (n) ). Assume that phi: a"e (n) x [0,a) -> [0,a) is a function such that phi(x, center dot) is an Orlicz function, phi(center dot, t) a A (a)(a"e (n) ) (the class of uniformly Muckenhoupt weights). Let w be an L-harmonic function on a"e (n) with 0 < C (1) a (c) 1/2 w a (c) 1/2 C (2), where C (1) and C (2) are positive constants. In this article, the author proves that the mapping is an isomorphism from the Musielak-Orlicz-Hardy space associated with , to the Musielak-Orlicz-Hardy space under some assumptions on phi. As applications, the author further obtains the atomic and molecular characterizations of the space associated with w, and proves that the operator is an isomorphism of the spaces and . All these results are new even when phi(x, t) a parts per thousand" t (p) , for all x a a"e (n) and t a [0,a), with p a (n/(n + mu(0)), 1) and some mu(0) a (0, 1].