Variants of Kato’s inequality and removable singularities

An inequality reminiscent of Kato’s inequality is presented. Motivated by this, we discuss some criteria to decide whether a singularity of the equation Δu=g in Ω/K comes from a Radon measure or not. As an application, we extend a lemma of H. Brezis and P. L. Lions on isolated singularities to the case where the singularity lies on a compact manifold. this author was supported by CAPES, Brazil, under the grant BEX 1187/99-6.