Multilinear Proofs for Convolution Estimates for Degenerate Plane Curves

Abstract

AbstractSuppose that γ ∈ C2 ([0, ∞)) is a real-valued function such that γ(0) = γ′(0) = 0, and γ″(t) ≈ tm−2, for some integer m ≥ 2. Let Γ(t) = (t, γ(t)), t > 0, be a curve in the plane, and let dλ = dt be a measure on this curve. For a function ƒ on R2, letAn elementary proof is given for the optimal Lp-Lq mapping properties of T.