For every p in (1, infinity), the maximal modulation of the line-restricted Hilbert transform along the parabola is bounded on Lp, uniformly over all lines.
Roos, Bounds for anisotropic Carleson operators
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The Hilbert transform along the parabola, the polynomial Carleson theorem and oscillatory singular integrals
For every p in (1, infinity), the maximal modulation of the line-restricted Hilbert transform along the parabola is bounded on Lp, uniformly over all lines.