Essential norm estimates for multilinear singular and fractional integrals

Abstract

We derive lower two-weight estimates for the essential norm (measure of noncompactness) for multilinear Hilbert and Riesz transforms, and Riesz potential operators in Banach function lattices. As a corollary we have appropriate results in weighted Lebesgue spaces. From these statements we conclude that there is no \((m+1)\)-tuple of weights \((v,w_1, \dots, w_m)\) for which these operators are compact from \(L^{p_1}_{w_1} \times \dots \times L^{p_m}_{w_m}\) to \(L^q_v\).