Singular integral operator, Hardy-Morrey space estimates for multilinear operators and Navier-Stokes equations

After establishing the molecule characterization of the Hardy–Morrey space, we prove the boundedness of the singular integral operator and the Riesz potential. We also obtain the Hardy–Morrey space estimates for multilinear operators satisfying certain vanishing moments. As an application, we study the existence and the uniqueness of the solutions to the Navier–Stokes equations for the initial data in the Hardy–Morrey space ℋ︁ℳ︁(p⩾n) for q as small as possible. Here, the Hardy–Morrey space estimates for multilinear operators are important tools.