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A note on restricted weak-type estimates for Bochner-Riesz operators with negative index in
Authors:Susana Gutié  rrez
Affiliation:Departamento de Matemáticas, Facultad de Ciencias, Universidad del País Vasco (UPV-EHU), Aptdo 644, 48080 Bilbao, Spain
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 $(p_0,q_0)$ and $(q_0', p_0')$, where $1/q_0=3/4+alpha /2$, $q_0=p_0'/3$ for $-3/2<alpha<0$ in the two-dimensional case and $1/q_0=(n+1+2alpha)/2n$, $q_0=(n-1)p_0'/(n+1),,$ for $-(n+ 1)/2<alpha<-1/2$ if $ngeq 3$.

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