Resumen de Endpoint bounds for a generalized Radon transform

Betsy Stovall

• 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.