Sharp estimates for the Bochner-Riesz operator of negative order in
Author:
Jong-Guk Bak
Journal:
Proc. Amer. Math. Soc. 125 (1997), 1977-1986
MSC (1991):
Primary 42B15
DOI:
https://doi.org/10.1090/S0002-9939-97-03723-4
MathSciNet review:
1371114
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Abstract | References | Similar Articles | Additional Information
Abstract: The Bochner-Riesz operator on
of order
is defined by
where denotes the Fourier transform and
if
, and
if
. We determine all pairs
such that
on
of negative order is bounded from
to
. To be more precise, we prove that for
the estimate
holds if and only if
, where
We also obtain some weak-type results for .
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Additional Information
Jong-Guk Bak
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306–3027
Address at time of publication:
Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Korea
Email:
bak@euclid.postech.ac.kr
DOI:
https://doi.org/10.1090/S0002-9939-97-03723-4
Received by editor(s):
October 3, 1995
Received by editor(s) in revised form:
December 19, 1995
Additional Notes:
The author’s research was partially supported by a grant from the Pohang University of Science and Technology
Communicated by:
Christopher D. Sogge
Article copyright:
© Copyright 1997
American Mathematical Society