A note on restricted weak-type estimates for Bochner-Riesz operators with negative index in ℝⁿ, 𝕟≥2

Gutiérrez, Susana

doi:10.1090/S0002-9939-99-05144-8

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

Proc. Amer. Math. Soc. 128 (2000), 495-501

DOI: https://doi.org/10.1090/S0002-9939-99-05144-8

Published electronically: June 24, 1999

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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 $(p_0,q_0)$ 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 $1/q_0=(n+1+2\alpha )/2n$, $q_0=(n-1)p_0’/(n+1),$ for $-(n+ 1)/2<\alpha <-1/2$ if $n\geq 3$.

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