Strongly singular integrals along curves

Details Strongly singular integrals along curves Strongly singular integrals along curves

2006-12-20

arxiv.org/abs/math/0612588v1

Mathematics

Classical Analysis and ODEs

10 pages

Scientific paper

In this article we obtain $L^2$ bounds for strongly singular integrals along
curves in $\R^d;$ our results both generalise and extend to higher dimensions
those obtained by Chandarana in the plane. Moreover, we show that the operators
in question are bounded from $L\log L$ to weak $L^1$ at the critical exponent
$\alpha=0.$

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