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Convolution estimates for some degenerate curves

Published online by Cambridge University Press:  24 October 2008

Yibiao Pan
Yibiao Pan
Affiliation:
Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA
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Let k ∈ R, k ≥ 3. Consider the curve of class C3 in R3 defined by

Let σk(t) = t(k−3)/6dt be the affine arclength measure on γk. Define the convolution operator T (= Tk) by

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 1 , July 1994 , pp. 143 - 146
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

REFERENCES

[1]Drury, S. W.. Degenerate curves and harmonic analysis. Math. Proc. Cambridge Phil. Soc. 108 (1990), 89–96.CrossRefGoogle Scholar
[2]Oberlin, D.. Convolution estimates for some measures on curves. Proc. Amer. Math. Soc. 99 (1987), 56–60.CrossRefGoogle Scholar
[3]Stein, E. M. and Weiss, G.. Introduction to Fourier analysis on Euclidean spaces (Princeton Univ. Press, 1971).Google Scholar
[4]Zygmund, A.. Trigonometric series (Cambridge Univ. Press, 1959).Google Scholar