Abstract
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.
Note
In memory of Brent Smith.
Citation
Yaryong Heo. Fëdor Nazarov. Andreas Seeger. "Radial Fourier multipliers in high dimensions." Acta Math. 206 (1) 55 - 92, 2011. https://doi.org/10.1007/s11511-011-0059-x
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