The Interpolation Theorem And Multilinear Fractional Integral Operator On Non-doubling Measure Spaces

This dissertation is devoted to the study of the interpolation theorem related to Hardy spaces and the boundedness of multilinear fractional integral operator and its commutators in non-doubling measure spaces. It consists of two chapters.The first chapter is concerning with the interpolation theorem on Hardy space associated toμ, whereμis the nonnegative Radon measure satisfying some growth condition. We establish a new interpolation theorem which improves the interpolation theorem of Tolsa in [25].Chapter 2 deals with a class of commutators generated by multilinear fractional integrals and RBMO(μ) functions. The boundedness of such operators on product of Lebesgue spaces withμare established, which extends the result of Chen and Sawyer in [3].