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Is the maximal function of a Lipschitz function continous

Stephen Buckley

Open publisher page 70 citations

Abstract

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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What this paper is about

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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OpenAlex reports 70 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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.

Key concepts: Lipschitz continuity, Counterexample, Mathematics, Context (archaeology), Property (philosophy), Homogeneous, Function (biology), Action (physics)

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