H1and BMO for certain locally doubling metric measure spaces of finite measure

H and Bmo for Certain Locally Doubling Metric Measure Spaces of Finite Measure

In a previous paper the authors developed a H−BMO theory for unbounded metric measure spaces (M, ρ, μ) of infinite measure that are locally doubling and satisfy two geometric properties, called “approximate midpoint” property and “isoperimetric” property. In this paper we develop a similar theory for spaces of finite measure. We prove that all the results that hold in the infinite measure case ...

Functions on Localized BMO Spaces over Doubling Metric Measure Spaces

Let X be a doubling metric measure space. In this paper, the authors introduce the notions of Property (M̃) and Property (P ) of X , prove that Property (M̃) implies Property (P ) and give some equivalent characterizations of Property (M̃) and Property (P ). If X has Property (P ), the authors then establish the boundedness of the Lusin-area function, which is defined via kernels modeled on the se...

Fine properties of sets of finite perimeter in doubling metric measure spaces

Marked Metric Measure Spaces

A marked metric measure space (mmm-space) is a triple (X , r,μ), where (X , r) is a complete and separable metric space and μ is a probability measure on X × I for some Polish space I of possible marks. We study the space of all (equivalence classes of) marked metric measure spaces for some fixed I . It arises as a state space in the construction of Markov processes which take values in random ...

Mappings of Finite Distortion between Metric Measure Spaces

We establish the basic analytic properties of mappings of finite distortion between proper Ahlfors regular metric measure spaces that support a (1, 1)-Poincaré inequality. As applications, we prove that under certain integrability assumption for the distortion function, the branch set of a mapping of finite distortion between generalized n-manifolds of type A has zero Hausdorff n-measure.