This is a very interesting paper that examines the conditions on the density for the hypersingular integrals
to exist. It is well known that it is sufficient that has a Hölder-continuous first derivative. This paper is concerned with finding weaker conditions and it is established that it is sufficient for (this is a Hadamard finite-part integral) that the even part of has a Hölder-continuous first derivative. A similar condition is found for (a Cauchy principal value). The non-trivial consequences of these results are discussed, particularly with regard to collocation at a point between two boundary elements.