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Spherical multipliers
V. Z. Meshkov M. V. Lomonosov Moscow State University
Abstract:
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 $(n-1-2\alpha)/(2n)<1/p<(n+1+2\alpha)/(2n)$.
Received: 26.06.1974
Citation:
V. Z. Meshkov, “Spherical multipliers”, Mat. Zametki, 23:1 (1978), 105–112; Math. Notes, 23:1 (1978), 58–62
Linking options:
https://www.mathnet.ru/eng/mzm8123 https://www.mathnet.ru/eng/mzm/v23/i1/p105
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Abstract page: | 188 | Full-text PDF : | 97 | First page: | 1 |
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