Open Access
2011 Radial Fourier multipliers in high dimensions
Yaryong Heo, Fëdor Nazarov, Andreas Seeger
Author Affiliations +
Acta Math. 206(1): 55-92 (2011). DOI: 10.1007/s11511-011-0059-x


Given a fixed p≠2, we prove a simple and effective characterization of all radial multipliers of $ \mathcal{F}{L^p}\left( {{\mathbb{R}^d}} \right) $, provided that the dimension d is sufficiently large. The method also yields new Lq space-time regularity results for solutions of the wave equation in high dimensions.

Funding Statement

Y. H. was supported by grants from the Korea Research Foundation and the National Research Foundation of Korea. F. N. and A. S. were supported in part by grants from the National Science Foundation.


In memory of Brent Smith.


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Yaryong Heo. Fëdor Nazarov. Andreas Seeger. "Radial Fourier multipliers in high dimensions." Acta Math. 206 (1) 55 - 92, 2011.


Received: 9 February 2009; Published: 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1219.42006
MathSciNet: MR2784663
Digital Object Identifier: 10.1007/s11511-011-0059-x

Primary: 42B15

Rights: 2011 © Institut Mittag-Leffler

Vol.206 • No. 1 • 2011
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