Products of Functions in H-rho(1) (x) and BMO rho (x) over RD-Spaces and Applications to Schrodinger Operators

摘要

Let (X, d, mu) be an RD-space, H-rho(1)(X), and BMO rho(X) be, respectively, the local Hardy space and the local BMO space associated with an admissible function rho. Under an additional assumption that there exists a specific generalized approximation of the identity, the authors prove that the product f x g of f is an element of H-rho(1) (X) and g is an element of BMO rho(X), viewed as a distribution, can be written into a sum of two bounded bilinear operators, respectively, from H-rho(1) (X) x BMO rho(X) into L-1(X) and from H-rho(1) (X) xBMO(rho)(X) into H-log(X), which is of wide generality. The authors also give out four applications of this result to Schrdinger operators, respectively, over different underlying spaces, where three of these applications are new.