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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On almost everywhere convergence of Bochner-Riesz means in higher dimensions


Author: Michael Christ
Journal: Proc. Amer. Math. Soc. 95 (1985), 16-20
MSC: Primary 42B25; Secondary 47G05
MathSciNet review: 796439
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Abstract: In $ {{\mathbf{R}}^n}$ define $ ({T_{\lambda ,r}}f)(\xi ) = \hat f(\xi )(1 - \left\vert {{r^{ - 1}}{\xi ^2}} \right\vert)_ + ^\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})$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0796439-7
PII: S 0002-9939(1985)0796439-7
Article copyright: © Copyright 1985 American Mathematical Society