Lp-Boundedness of a Singular Integral Operator

Abstract

AbstractLet b(t) be an L∞ function on R, Ω(y′) be an H1 function on the unit sphere satisfying the mean zero property (1) and Qm(t) be a real polynomial on R of degree m satisfying Qm(0) = 0. We prove that the singular integral operatoris bounded in Lp(Rn) for 1 < p < ∞, and the bound is independent of the coefficients of Qm(t).