Restriction of the Fourier transform to some oscillating curves

2017/01/02 by Chen, Xianghong, Fan, Dashan, Wang, Lifeng
#42B10 #42B99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.00477

Abstract

Let ϕ be a smooth function on a compact interval I. Let γ(t)= (t,t²,⋯,t^n-1,ϕ(t)). In this paper, we show that (∫_I | f(γ(t))|^q |ϕ⁽ⁿ⁾(t)|^(2)/(n(n+1)) dt)^1/q≤ C‖f‖_{L^p(\mathbb Rⁿ)} holds in the range 1≤ p

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