Boundedness of averaging operators on geometrically doubling metric spaces

2017/10/11 by J. M. Aldaz, Aldaz, J. M.
Mathematics · #Advanced Harmonic Analysis Research #Geometric Analysis and Curvature Flows #Advanced Banach Space Theory

paper · doi:10.48550/arxiv.1710.04233

Abstract

We prove that averaging operators are uniformly bounded on L¹ for all geometrically doubling metric measure spaces, with bounds independent of the measure. From this result, the L¹ convergence of averages as r → 0 immediately follows.

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