Carleson Measure Characterization And Application Of BM0-type Space Related To Generalized Schr(?)dinger Operator

In this thesis,we introduced the definition and basic properties of the BMO-type space associated with the generalized Schr(?)dinger operator and the Carleson measure.The concept and properties of the area function and maximal operator associated with the heat semigroup and the Poisson semigroup are also introduced.Then,we introduced two families of Carleson measures {dvh,k} and {dvp,k} generated by the heat semigroup {e-tL} and the Poisson semigroup {e-t(?)},respectively.By the regularities of semigroups,we established the Carleson measure characterizations of BMO-type spaces BMOC(Rn)associated with the generalized Schr(?)dinger operators.After that,used the k-order perturbation formula associated with the heat semigroup,and the k-order perturbation formula related to the Poisson semigroup,we discussed the boundedness of the area function and the semigroup maximal operator on BMOL(Rn)associated with the generalized Schr(?)dinger operators.