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Regularity of Maximal Operators: Recent Progress and Some Open Problems

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New Trends in Applied Harmonic Analysis, Volume 2

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

This is an expository paper on the regularity theory of maximal operators, when these act on Sobolev and BV functions, with a special focus on some of the current open problems in the topic. Overall, a list of fifteen research problems is presented. It summarizes the contents of a talk delivered by the author in the CIMPA 2017 Research School—Harmonic Analysis, Geometric Measure Theory, and Applications, in Buenos Aires, Argentina.

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Acknowledgements

The author acknowledges support from CNPq–Brazil grants 305612/2014-0 and 477218/2013-0, and FAPERJ grant E-26/103.010/2012. The author is thankful to José Madrid and João Pedro Ramos for reviewing the manuscript and providing valuable feedback. The author is also thankful to all of the members of the Scientific and Organizing Committees of the CIMPA 2017 Research School—Harmonic Analysis, Geometric Measure Theory and Applications, in Buenos Aires, Argentina, for the wonderful event.

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Authors and Affiliations

  1. IMPA—Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320, Brazil

    Emanuel Carneiro

  2. ICTP - The Abdus Salam International Centre for Theoretical Physics, Strada Costiera, 11, 34151, Trieste, Italy

    Emanuel Carneiro

Authors
  1. Emanuel Carneiro
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Correspondence to Emanuel Carneiro .

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Editors and Affiliations

  1. Vanderbilt University, Nashville, TN, USA

    Akram Aldroubi

  2. Department of Mathematics (FCEyN), Universidad de Buenos Aires, Buenos Aires, Argentina

    Carlos Cabrelli

  3. Department of Mathematics (LAMA), Université Paris-Est Créteil, Creteil, Paris, France

    Stéphane Jaffard

  4. Department of Mathematics (FCEyN), Universidad de Buenos Aires, Buenos Aires, Argentina

    Ursula Molter

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Carneiro, E. (2019). Regularity of Maximal Operators: Recent Progress and Some Open Problems. In: Aldroubi, A., Cabrelli, C., Jaffard, S., Molter, U. (eds) New Trends in Applied Harmonic Analysis, Volume 2. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-32353-0_3

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