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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Differentiation of Besov spaces and the Nikodym maximal operator
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by Jason Murcko PDF
Proc. Amer. Math. Soc. 145 (2017), 2139-2153 Request permission

Abstract:

We study several questions related to differentiation of integrals for Besov spaces relative to the basis $\mathcal {R}$ of arbitrarily oriented rectangular parallelepipeds in $\mathbb {R}^{d}$, $d \geq 2$. We improve on positive and negative differentiation results of Aimar, Forzani, and Naibo and on capacitary and dimensional bounds for exceptional sets of Naibo. Our main tool in obtaining these improvements involves showing that bounds for the Nikodym maximal operator can be used to deduce boundedness properties of the local maximal operator associated to $\mathcal {R}$.
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Additional Information
  • Jason Murcko
  • Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706
  • Email: jmurcko@gmail.com
  • Received by editor(s): July 11, 2016
  • Published electronically: December 30, 2016
  • Additional Notes: The author would like to thank his advisor, Andreas Seeger, for his guidance and support
    The author was supported in part by the National Science Foundation.
  • Communicated by: Alexander Iosevich
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 2139-2153
  • MSC (2010): Primary 42B25, 42B35
  • DOI: https://doi.org/10.1090/proc/13396
  • MathSciNet review: 3611327