Atomic decomposition of Besov-type and Triebel-Lizorkin-type spaces (Q1955511)

Let \(B^{s,\tau}_{p,q} (\mathbb R^n)\) and \(F^{s,\tau}_{p,q} (\mathbb R^n)\) be the Morrey versions of the nowadays well-known scales \(B^s_{p,q} (\mathbb R^n)\) and \(F^s_{p,q} (\mathbb R^n)\). Here, \(0<p,q \leq \infty\), \(s\in \mathbb R\), \(\tau \geq 0\). It is the main aim of the paper to extend the atomic representation theorems for \(B^s_{p,q} (\mathbb R^n)\) and \(F^s_{p,q} (\mathbb R^n)\) to their Morreyfied generalizations.