Resumen de Sobolev spaces associated to singular and fractional Radon transforms

Brian Street

• The purpose of this paper is to study the smoothing properties (in Lp Sobolev spaces) of operators of the form f↦ψ(x)∫f(γt(x))K(t)dt, where γt(x) is a C∞ function defined on a neighborhood of the origin in (t,x)∈RN×Rn, satisfying γ0(x)≡x, ψ is a C∞ cut-off function supported on a small neighborhood of 0∈Rn, and K is a "multi-parameter fractional kernel" supported on a small neighborhood of 0∈RN...