abstract: This talk is about a class of weakly singular integro-differential operators. More precisely, we assume that the Fourier sine transform of the convolution kernel has a suitable behaviour at infinity. Some concrete examples of such kernels can be given, presenting an integrable singularity at the origin. We establish a local Carleman estimate, which enables us to show the unique continuation property for this class of operators. These results are contained in a joint paper with Piermarco Cannarsa.