Remarks on Chemin's space of homogeneous distributions

Abstract

AbstractThis paper focuses on Chemin's space of homogeneous distributions, which was introduced to serve as a basis for the realizations of subcritical homogeneous Besov spaces. We will discuss how this construction fails in multiple ways for supercritical spaces. In particular, we study its intersection with various Banach spaces X, namely supercritical homogeneous Besov spaces and the Lebesgue space . For each X, we investigate whether the intersection is dense in X. If it is not, then we study its closure and prove that the quotient is not separable and that C is not complemented in X.