Abstract
We use wavelets based on a modification of the Geronimo-Hardin-Massopust construction to define localized extension/restriction operators from half-spaces to their full spaces/boundaries respectively. These operations are continuous in Sobolev and Morrey space norms. We also prove estimates for multiresolution projections of pointwise products of functions in these spaces. These are two of the key steps in extending results of Federbush (1993) and of Cannone and Meyer (1995) concerning solutions of Navier-Stokes with initial data in Sobolev and Morrey spaces to the case of half spaces and, ultimately, to more general domains with boundary. (Author)