The Lp-improving properties of convolution operators with measures supported on space curves have been studied by various authors. If the underlying curve is non-degenerate, the convolution with the (Euclidean) arclength measure is a bounded operator from L3/2()3 into L2(3). Drury suggested that in case the underlying curve has degeneracies the appropriate measure to consider should be the affine arclength measure and the obtained a similar result for homogeneous curves ta?’(t, t2, tk), t >0 for k a‰￥ 4. This was further generalized by Pan to curves t a?’ (t, tk, tt), t > 0 for l < k < l, k+l a‰￥ 5. In this article, we will extend Pan's result to (smooth) compact curves of finite type whose tangents never vanish. In addition, we give an example of a flat curve with the same mapping properties.
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