A theorem on measures in dimension 2 and applications to vortex sheets

We find conditions under which measures belong to H⁻¹(R²)$H^{-1}({\mathbb{R}}^2)$. Next we show that measures generated by the Prandtl, Kaden as well as Pullin spirals, objects considered by physicists as incompressible flows generating vorticity, satisfy assumptions of our theorem, thus they are (locally) elements of H⁻¹(R²)$H^{-1}({\mathbb{R}}^2)$. Moreover, as a by-product, we prove an embedding of the space of Morrey type measures in H⁻¹$H^{-1}$.