A class of nonhomogeneous singular integrals in Rn

AbstractLet {δt}t>0 be a nonisotropic dilation group on Rn, let ρ be a distance function on Rn which is homogeneous with respect to {δt}t>0, and for f∈C0∞(Rn) define Tf=[p.v.ρ(·)−αei/|·|β]∗f, where α and β are positive parameters. We give necessary and sufficient conditions on p, α and β for which T extends to a bounded linear operator on Lp(Rn)