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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel


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2299-3274
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Fractional Maximal Functions in Metric Measure Spaces

Toni Heikkinen / Juha Lehrbäck / Juho Nuutinen / Heli Tuominen
Published Online: 2013-05-28 | DOI: https://doi.org/10.2478/agms-2013-0002

Abstract

We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to Hölder continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous.

Keywords: Fractional maximal function; fractional Sobolev space; Campanato space; metric measure space

MSC: 42B25; 46E35

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About the article

Received: 2013-01-30

Accepted: 2013-05-10

Published Online: 2013-05-28


Citation Information: Analysis and Geometry in Metric Spaces, Volume 1, Pages 147–162, ISSN (Online) 2299-3274, DOI: https://doi.org/10.2478/agms-2013-0002.

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