L^q-theory of a singular “winding” integral operator arising from fluid dynamics

We analyze in classical L q (R n)-spaces, n = 2 or n = 3, 1 <q<∞, a singular integral operator arising from the linearization of a hydrodynamical problem with a rotating obstacle. The corresponding system of partial differential equations of second order involves an angular derivative which is not subordinate to the Laplacian. The main tools are Littlewood–Paley theory and a decomposition of the singular kernel in Fourier space.