Abstract
We prove that for radial Fourier multipliers supported compactly away from the origin, is restricted strong type if is in , in the range . We also prove an characterization for radial Fourier multipliers in four dimensions; namely, for radial Fourier multipliers supported compactly away from the origin, is bounded on if and only if is in , in the range . Our method of proof relies on a geometric argument that exploits bounds on sizes of multiple intersections of 3-dimensional annuli to control numbers of tangencies between pairs of annuli in three and four dimensions.
Citation
Laura Cladek. "Radial Fourier multipliers in $\mathbb{R}^3$ and $\mathbb{R}^4$." Anal. PDE 11 (2) 467 - 498, 2018. https://doi.org/10.2140/apde.2018.11.467
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