Is the maximal function of a Lipschitz function continous?
Buckley, Stephen M. (1999) Is the maximal function of a Lipschitz function continous? Annales Academiæ Scientiarum Fennicæ Mathematica, 24 . pp. 519-528. ISSN 1798-2383
We examine the action of the maximal operator on Lipschitz and Hölder functions in the context of homogeneous spaces. Boundedness results are proven for spaces satisfying an annular decay property and counterexamples are given for some other spaces. The annular decay property is defined and investigated.
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