L−improving Properties for Measures on R Supported on Homogeneous Surfaces in Some Non Elliptic Cases


In this paper we study convolution operators Tμ with measures μ in R of the form μ (E) = ∫ B χE (x, φ (x)) dx, where B is the unit ball of R, and φ is a homogeneous polynomial function. If infh∈S1 ∣∣det (d2xφ (h, .))∣∣ vanishes only on a finite union of lines, we prove, under suitable hypothesis, that Tμ is bounded from L into L if ( 1 p , 1 q ) belongs to… (More)