Hermite expansions on $\textbf {R}^ n$ for radial functions
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- by S. Thangavelu PDF
- Proc. Amer. Math. Soc. 118 (1993), 1097-1102 Request permission
Abstract:
It is proved that the Riesz means $S_R^\delta f, \delta > 0$, for the Hermite expansions on ${\mathbb {R}^n}, n \geqslant 2$, satisfy the uniform estimates ${\left \| {S_R^\delta f} \right \|_p} \leqslant C{\left \| f \right \|_p}$ for all radial functions if and only if $p$ lies in the interval $2n/(n + 1 + 2\delta ) < p < 2n/(n - 1 - 2\delta )$.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 1097-1102
- MSC: Primary 42C10; Secondary 33C45, 42C15
- DOI: https://doi.org/10.1090/S0002-9939-1993-1137236-7
- MathSciNet review: 1137236