Distribution of points and Hardy type inequalities in spaces of homogeneous type

Abstract

In the setting of spaces of homogeneous type, we study some Hardy type inequalities, which notably appeared in the proofs of local T(b) theorems as in [AR]. We give some suffi cient conditions ensuring their validity, related to the geometry and distribution of points in the homogeneous space. We study the relationships between these conditions and give some examples and counterexamples in the complex plane.

References in corpus (2)

• A proof of the local $Tb$ Theorem for standard Calderón-Zygmund operators
• Local Tb theorems and Hardy inequalities

Cited by in corpus (1)

• Fractional maximal functions in metric measure spaces