A remark on the Hardy-Littlewood maximal functions

We investigate the magnitude relation of the non-centered Hardy-Littlewood maximal operators and centered one. By using a discretization technique, we prove two facts: the first one is that the space is ultrametric if and only if the two maximal operators are identical for all discrete measure; the...

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Bibliographic Details
Published in:arXiv.org 2022-11
Main Author: Wu-yi, Pan
Format: Article
Language:English
Subjects:
Riemann manifold
Online Access:Get full text
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Summary:We investigate the magnitude relation of the non-centered Hardy-Littlewood maximal operators and centered one. By using a discretization technique, we prove two facts: the first one is that the space is ultrametric if and only if the two maximal operators are identical for all discrete measure; the second is, the uncentred maximal operator is strictly greater than the centered one if \((M,d_g)\) is a Riemannian manifold and \(\mu\) is the Riemannian volume measure.
ISSN:2331-8422