A note on the “hyperbolic” Bochner-Riesz means
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- by Anthony Carbery PDF
- Proc. Amer. Math. Soc. 92 (1984), 397-400 Request permission
Abstract:
We consider the ${L^p}({{\mathbf {R}}^2})$ boundedness properties of the Fourier multiplier $m({\xi _1},{\xi _2}) = (1 - \xi _1^2\xi _2^2)_ + ^\alpha {\text { for }}\alpha > 0$. We prove that if $\alpha \geqslant \frac {1}{2}$, then $m$ is bounded on ${L^p}$, $1 < p < \infty$, and that if $\alpha > 0$, then $m$ is bounded on ${L^p}$, $\frac {4}{3} \leqslant p \leqslant 4$.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 397-400
- MSC: Primary 42B15
- DOI: https://doi.org/10.1090/S0002-9939-1984-0759661-0
- MathSciNet review: 759661