H~p(μ) Space And Campanato Space For Certain Nondoubling Metric Measure Spaces

Let (M, ρ,μ)be a metric measure space with several geometry properties, in which themeasure μ is locally doubled and μ (M)=∞. In this paper we prove that an inequality ofJohn-Nirenberg type holds for functions in Campanato space and Campanato space is thedual of H~p(μ)space.There are four chapters in this paper.In the first chapter, we briefly describe some research results of function spaces andsingular integral operators, some assumptions used in this paper, and the structure of thispaper.In the second chapter, we introduce the geometry properties and related lemmas of(M, ρ,μ).In the third chapter, we introduce the definition of Campanato space and prove theJohn-Nirenberg type inequalitie of the Campanato space.In the fifth chapter, we introduce the definition of H~p(μ)(n/(n+1)<p<1)space anddiscuss the dual property of H~p(μ)space.