Anisotropic Interpolation Theorems Of Musielak-orlicz Type

The real-variable theory of Hardy spaces plays an important role in harmonic analysis,which has important applications in various fields of analysis and partial differential equations.Let φ be an anisotropic Musielak-Orlicz function with growth assumptions and A an expansive dilation.We mainly study anisotropic interpolation theorems of MusielakOrlicz type.Firstly,we introduce the background,current research situation and the main results of Musielak-Orlicz spaces and weighted anisotropic Hardy spaces and related interpolation theorems.Then we recall the definitions of the anisotropic Musielak-Orlicz function satisfying the growth conditions and related function spaces.Finally,we obtain two interpolation theorems on the related function spaces.Precisely,by the boundedness of sublinear operator T on weighted anisotropic Hardy spaces and weighted(weak)Lebesgue spaces,we can further obtain the boundedness of T on anisotropic MusielakOrlicz spaces.