Betsy Stovall

Endpoint bounds for a generalized Radon transform

We prove that convolution with affine arclength measure on the curve parametrized by h(t) := (t, t2, . . . , tn) is a bounded operator from Lp(Rn) to Lq(Rn) for the full conjectured range of exponents, improving on a result due to M. Christ. We also obtain nearly sharp Lorentz space bounds.

Endpoint Lp→Lq bounds for integration along certain polynomial curves

We establish strong-type endpoint

Uniform Lp-improving for weighted averages on curves

L^p(\mathbb R^d) \to L^q(\mathbb R^d)

Blowup behaviour for the nonlinear Klein–Gordon equation

bounds for the operator given by convolution with affine arclength measure on polynomial curves for

Scattering for the cubic Klein–Gordon equation in two space dimensions

d \geq 4

Some Problems in Harmonic Analysis

. The bounds established depend only on the dimension

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

d

Uniform estimates for the X-ray transform restricted to polynomial curves

and the degree of the polynomial.

Quasi-extremals for convolution with surface measure on the sphere

We define variable parameter analogues of the affine arclength measure on curves and prove near-optimal

Uniform estimates for Fourier restriction to polynomial curves in

L^p