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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Weak type estimates for Bochner-Riesz spherical summation multipliers


Authors: Sagun Chanillo and Benjamin Muckenhoupt
Journal: Trans. Amer. Math. Soc. 294 (1986), 693-703
MSC: Primary 42B20; Secondary 44A15
MathSciNet review: 825730
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Abstract: We consider the Bochner-Riesz multiplier

$\displaystyle \widehat{{T_\delta }f}(\xi ) = {(1 - {\left\vert \xi \right\vert^2})^\delta } + \hat f(\xi ),\qquad \delta > 0,$

where $ \widehat{}$ denotes the Fourier transform. It is shown that the multiplier operator $ {T_\delta }$ is weak type $ ({p_0},\,{p_0})$ acting on $ {L^{p0}}({{\mathbf{R}}^n})$ radial functions, where $ {p_0}$ is the critical value $ 2n/(n + 1 + 2\delta )$.

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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0825730-6
PII: S 0002-9947(1986)0825730-6
Article copyright: © Copyright 1986 American Mathematical Society