Convolution of a measure with itself and a restriction theorem
Authors:
JongGuk Bak and David McMichael
Journal:
Proc. Amer. Math. Soc. 125 (1997), 463470
MSC (1991):
Primary 42B10
MathSciNet review:
1350932
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Abstract: Let and be the measure defined by . Let denote the measure obtained by restricting to the set . We prove estimates on . As a corollary we obtain results on the restriction to of the Fourier transform of functions on for , .
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 L. Hörmander, Oscillatory integrals and multipliers on , Ark. Mat. 11 (1973), 111. MR 49:5674
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 R. O'Neil, Convolution operators and spaces, Duke Math. J. 30 (1963), 129142. MR 26:4193
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 P. Tomas, Restriction theorems for the Fourier transform, in Proceedings of Symposia in Pure Mathematics, Vol. 35, pp. 111114, Amer. Math. Soc., 1979. MR 81d:42029
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 A. Zygmund, On Fourier coefficients and transforms of two variables, Studia Math. 50 (1974), 189201. MR 52:8788
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Additional Information
JongGuk Bak
Affiliation:
Department of Mathematics, Pohang University of Science and Technology, Pohang 790784, Korea
Email:
bak@euclid.postech.ac.kr
David McMichael
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306
DOI:
http://dx.doi.org/10.1090/S0002993997035697
PII:
S 00029939(97)035697
Received by editor(s):
April 13, 1995
Received by editor(s) in revised form:
August 10, 1995
Additional Notes:
The first author was supported in part by a grant from TGRC–KOSEF of Korea.
Communicated by:
J. Marshall Ash
Article copyright:
© Copyright 1997
American Mathematical Society
