THE CHARACTERIZATIONS OF HARDY SOBOLEVSPACES BY FRACTIONAL SQUARE FUNCTIONSRELATED TO SCHR?DINGER OPERATORS

摘要

Let L = + V be a Schrdinger operator, where the potentialV satisfies the reverse H"older condition. In this paper, via theheat semigroup e tL and the Poisson semigroup e tL,we introduce several classes of fractional square functionsassociated with L including the Litttlewood Paley g-function,the area integral and the g*-function, respectively. Bythe regularities of semigroup, we establish several squarefunction characterizations of the Hardy space and the Hardy Sobolevspace related to the Schrdinger operator.