A simplified two-ends Furstenberg inequality holds for transversal curve families and yields L6 Fourier decay R^{2-5s/2+ε} for s-Frostman measures on convex curves when s≤2/3.
Two-ends Furstenberg estimates in the plane
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abstract
We prove two-ends Furstenberg estimates in the plane for a Katz-Tao $(\delta,t)$-set of lines, for general $t\in[0,2]$.
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Two-ends Furstenberg inequality for transversal families and applications to Fourier decay
A simplified two-ends Furstenberg inequality holds for transversal curve families and yields L6 Fourier decay R^{2-5s/2+ε} for s-Frostman measures on convex curves when s≤2/3.