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

 

Hermite expansions on $ {\bf R}\sp n$ for radial functions


Author: S. Thangavelu
Journal: Proc. Amer. Math. Soc. 118 (1993), 1097-1102
MSC: Primary 42C10; Secondary 33C45, 42C15
MathSciNet review: 1137236
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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\Vert {S_R^\delta f} \right\Vert _p} \leqslant C{\left\Vert f \right\Vert _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 )$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1137236-7
PII: S 0002-9939(1993)1137236-7
Article copyright: © Copyright 1993 American Mathematical Society