A New Scale of Function Spaces Characterizing Homogeneous Besov Spaces

Abstract

Abstract We introduce and study a new scale of function spaces that characterize the homogeneous Besov spaces $$\dot{\text {B}}^{\beta }_{p,q}$$ B ˙ p , q β , hence completing earlier work by Ullrich. These new spaces include the ones introduced by Barton and Mayboroda, and systematically studied by Amenta under the name of weighted $$\textrm{Z}$$ Z -spaces, for the purpose of boundary value problems with $$\dot{\text {B}}^{\beta }_{p,p}$$ B ˙ p , p β data. They are the counterparts to the weighted tent spaces with Whitney averages, developed by Huang, and arise as their real interpolants. We describe their functional analytic properties: completeness, duality, embeddings, as well as their real and complex interpolants.