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

2012/01/26 by Routin, Eddy
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1201.5449

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.

Related

• Local Tb theorems and Hardy inequalities
• A review of Hardy inequalities
• Hardy-Hilbert type inequalities on homogeneous groups-An introduction and generalization to the kernel case
• A survey of Hardy type inequalities on homogeneous groups
• Hardy classes, integral operators, and duality on spaces of homogeneous type