Traces of functions in Hardy and Besov spaces on Lipschitz domains with applications to compensated compactness and the theory of Hardy and Bergman type spaces
a Department of Mathematics, University of Virginia, Kerchof Hall, Charlottesville, VA 22904, USA b Department of Mathematics, University of Missouri-Columbia, Mathematical Sciences Building, Columbia, MO 65211, USA
Abstract:
In this paper we study conditions guaranteeing that functions defined on a Lipschitz domain Ω have boundary traces in Hardy and Besov spaces on ∂Ω. In turn these results are used to develop a new approach to the theory of compensated compactness and the theory of non-locally convex Hardy and Bergman type spaces.