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A note on restricted weak-type estimates for Bochner-Riesz operators with negative index in $\mathbb{R}^n$ , $n\geq 2$

Author(s): Susana Gutiérrez
Journal: Proc. Amer. Math. Soc. 128 (2000), 495-501.
MSC (1991): Primary 42B15
Posted: June 24, 1999
MathSciNet review: 1641626
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Abstract: It is shown that the Bochner-Riesz operator on $\mathbb{R}^n$ of negative order $\alpha$ is of restricted weak type in the critical points and , where $1/q_0=3/4+\alpha /2$ , for $-3/2<\alpha<0$ in the two-dimensional case and $1/q_0=(n+1+2\alpha)/2n$ , $q_0=(n-1)p_0'/(n+1),\,$ for $-(n+ 1)/2<\alpha<-1/2$ if $n\geq 3$ .

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