Anisotropic Hardy Space, With Non-doubling Measures

In this thesis,motived by the results for non-doubling measures obtained by X.Tolsa and the anistropic Hardy spaces investigated by M.Bonik and Lan Senhua etc.,which enjoy some basic properties of classical Hardy spaces,we introduce the definition of anistropic atomic block under the non-doubling condtion and thus obtain the anistropic Hardy spaces for non-doubling measures and the atomic decomposition of the spaces H_A¹(μ),and duality of these Hardy spaces RBMO_A(μ).Then by the atomic characterization of the anistropic Hardy spaces for non-doubling measures and the properties of the coefficients K_Bj,BN,it is proved that the Calder(?)n-Zygmund operators are bounded from H_A¹(μ) into L¹(μ) and from L^∞(μ) into RBMO_A(μ).At the last,we introduced the fractional integral operators under the anistropic and non-doubling measures conditions and show the bounded result of these operators,that is, the famous Hardy-Littlewood-Sobolev inequlity.