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Convolution estimates for some measures on curves. Proc. Amer. Math. Soc. 99 (1987), no. 1, 56–60.1088-6826 Let I be a closed interval in R, and suppose that the real-valued functions ϕ1 and ϕ2 are both polynomial functions or both trigonometric functions on I. Suppose that the vectors of derivatives (ϕ (2) 1 (s), ϕ(2) s (s)) and (ϕ (3) 1 (t), ϕ(3) 2 (t)) span R2 for any s and t in I. Let λ be the measure on R3 defined by 〈λ, g 〉 = ∫ I g(t, ϕ1(t), ϕ2(t)) dt. Then λ ∗ L3/2 ⊂ L2. The proof of this result is pleasantly clean and simple—it uses van der Corput’s lemma (of course), complex interpolation, and intelligence. Some absolute value signs outside complex Γ-functions are missing, but do not impede understanding

Year: 2013

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