Discrete decomposition of homogeneous mixed-norm Besov spaces

Source abstract

One of the most influential contributions of Frazier and Jawerth is the construction of the discrete decomposition transformation, the so-called φ \varphi -transform, on spaces of distributions. In this article we introduce and study homogeneous mixed-norm Besov spaces. Furthermore we obtain a mixed-norm extension of the φ \varphi -transform in this development. This discrete decomposition is new even for inhomogeneous mixed-norm Besov spaces and so we also adapt our results to the inhomogeneous case.