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Beyond Local Maximal Operators

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Abstract

We obtain (essentially sharp) boundedness results for certain generalized local maximal operators between fractional weighted Sobolev spaces and their modifications. Concrete boundedness results between well known fractional Sobolev spaces are derived as consequences of our main result. We also apply our boundedness results by studying both generalized neighbourhood capacities and the Lebesgue differentiation of fractional weighted Sobolev functions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Jyvaskyla, P.O. Box 35, FI-40014, Jyvaskyla, Finland

    Hannes Luiro & Antti V. Vähäkangas

Authors
  1. Hannes Luiro
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  2. Antti V. Vähäkangas
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Corresponding author

Correspondence to Antti V. Vähäkangas.

Additional information

H.L. was supported by the Academy of Finland, grant no. 259069.

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Luiro, H., Vähäkangas, A.V. Beyond Local Maximal Operators. Potential Anal 46, 201–226 (2017). https://doi.org/10.1007/s11118-016-9581-y

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  • DOI: https://doi.org/10.1007/s11118-016-9581-y

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