Spyridon Dendrinos

Fourier restriction to polynomial curves I: a geometric inequality

We prove a Fourier restriction result for general polynomial curves in

Uniform estimates for the local restriction of the Fourier transform to curves

{\Bbb R}^d

An affine-invariant inequality for rational functions and applications in harmonic analysis

. Measuring the Fourier restriction with respect to the affine arclength measure of the curve, we obtain a universal estimate for the class of all polynomial curves of bounded degree. Our method relies on establishing a geometric inequality for general polynomial curves which is of interest in its own right. Applications of this geometric inequality to other problems in euclidean harmonic analysis have recently been established.

Universal L p improving for averages along polynomial curves in low dimensions

We prove sharp estimates, with respect to the affine arclength measure, for the restriction of the Fourier transform to a class of curves in R that includes curves of finite type. This measure possesses certain invariance and mitigation properties which are important in establishing uniform results.

Uniform bounds for convolution and restricted X-ray transforms along degenerate curves

We extend an affine-invariant inequality for vector polynomials established by Dendrinos and Wright to general rational functions. As a consequence we obtain sharp universal estimates for various problems in Euclidean harmonic analysis defined with respect to the so-called affine arc-length measure.