Boundedness of averaging operators on geometrically doubling metric spaces
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🧮 math.CA
keywords
averagingdoublinggeometricallymeasuremetricoperatorsspacesaverages
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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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