Abstract
We give a simple necessary and sufficient condition for maximal operators associated with radial Fourier multipliers to be bounded on Lprad and Lp for certain p greater than 2. The range of exponents obtained for the Lprad characterization is optimal for the given condition. The Lp characterization is derived from an inequality of Heo, Nazarov, and Seeger regarding a characterization of radial Fourier multipliers.
| Original language | English |
|---|---|
| Pages (from-to) | 1077-1085 |
| Number of pages | 9 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 145 |
| Issue number | 3 |
| Online published | 18 Nov 2016 |
| DOIs | |
| Publication status | Published - Mar 2017 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2016 American Mathematical Society.
Funding
This paper will be a part of the author?s Ph.D. thesis. Part of this research was carried out while the author was visiting the Hausdorff Research Institute for Mathematics (HIM) in Bonn. The author would like to thank HIM and the organizers of the trimester program on Harmonic Analysis and Partial Differential Equations for their hospitality and generous support during the visit. This work was supported in part by the National Science Foundation.
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