On almost everywhere convergence of Bochner-Riesz means in higher dimensions
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- by Michael Christ PDF
- Proc. Amer. Math. Soc. 95 (1985), 16-20 Request permission
Abstract:
In ${{\mathbf {R}}^n}$ define $({T_{\lambda ,r}}f)(\xi ) = \hat f(\xi )(1 - \left | {{r^{ - 1}}{\xi ^2}} \right |)_ + ^\lambda$. If $n \geq 3$, $\lambda > \tfrac {1}{2}(n - 1)/(n + 1)$ and $2 \leq p < 2n/(n - 1 - 2\lambda )$, then ${\lim _{r \to \infty }}{T_{\lambda ,r}}f(x) = f(x)$ a.e. for all $f \in {L^p}({{\mathbf {R}}^n})$.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 16-20
- MSC: Primary 42B25; Secondary 47G05
- DOI: https://doi.org/10.1090/S0002-9939-1985-0796439-7
- MathSciNet review: 796439