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

 

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


Author: Susana Gutiérrez
Journal: Proc. Amer. Math. Soc. 128 (2000), 495-501
MSC (1991): Primary 42B15
Published electronically: 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 $(p_0,q_0)$ 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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Additional Information

Susana Gutiérrez
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad del País Vasco (UPV-EHU), Aptdo 644, 48080 Bilbao, Spain
Email: mtbgugrs@lg.ehu.es

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05144-8
PII: S 0002-9939(99)05144-8
Received by editor(s): March 29, 1998
Published electronically: June 24, 1999
Additional Notes: Supported by a grant from Spanish Ministry of Education and Sciences.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1999 American Mathematical Society