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A characterization of maximal operators associated with radial fourier multipliers


Author: Jongchon Kim
Journal: Proc. Amer. Math. Soc. 145 (2017), 1077-1085
MSC (2010): Primary 42B15, 42B25
DOI: https://doi.org/10.1090/proc/13445
Published electronically: November 18, 2016
MathSciNet review: 3589308
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Abstract: We give a simple necessary and sufficient condition for maximal operators associated with radial Fourier multipliers to be bounded on $ L^p_{rad}$ and $ L^p$ for certain $ p$ greater than $ 2$. The range of exponents obtained for the $ L^p_{rad}$ characterization is optimal for the given condition. The $ L^p$ characterization is derived from an inequality of Heo, Nazarov, and Seeger regarding a characterization of radial Fourier multipliers.


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Additional Information

Jongchon Kim
Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
Email: jkim@math.wisc.edu

DOI: https://doi.org/10.1090/proc/13445
Received by editor(s): November 17, 2014
Published electronically: November 18, 2016
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2016 American Mathematical Society