Boundedness of averaging operators on geometrically doubling metric spaces (1710.04233v2)

Published 11 Oct 2017 in math.CA

Abstract: We prove that averaging operators are uniformly bounded on $L^1$ for all geometrically doubling metric measure spaces, with bounds independent of the measure. From this result, the $L^1$ convergence of averages as $r \to 0$ immediately follows.

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Authors (1)

J. M. Aldaz

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