Geodesic
Spherical multipliers
Matematičeskie zametki, Tome 23 (1978) no. 1, pp. 105-112

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It is proven in the paper that if function $f(x)\in L^p(R^n)$, where $1/p>1/2+1/(n+1)$, then the restriction of the Fourier transform $\widehat{f}(\xi)$ to the unit sphere $S^{n-1}$ lies in $L^2(S^{n-1})$. As was shown by Fefferman [1], it follows from this that, when $\alpha>(n-1)/(2(n+1))$, the Riesz–Bochner multiplieragr acts in $L^p(R^n)$, if $(n-1-2\alpha)/(2n)1/p(n+1+2\alpha)/(2n)$. 
@article{MZM_1978_23_1_a10,
     author = {V. Z. Meshkov},
     title = {Spherical multipliers},
     journal = {Matemati\v{c}eskie zametki},
     pages = {105--112},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_1_a10/}
}
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V. Z. Meshkov. Spherical multipliers. Matematičeskie zametki, Tome 23 (1978) no. 1, pp. 105-112. http://geodesic.mathdoc.fr/item/MZM_1978_23_1_a10/