Some characterizations of variable Besov-type spaces (Q2516302)

The well-known spaces \(B^s_{p,q}\) and \(F^s_{p,q}\) in \(\mathbb R^n\) and their Morrey generalizations \(B^{s,\tau}_{p,q}\) and \(F^{s,\tau}_{p,q}\) have been generalized to corresponding spaces with variable parameters, in particular \(B^{s(\cdot), \tau(\cdot)}_{p(\cdot), q(\cdot)}\). The paper contributes to this theory dealing in particular with characterizations in terms of \(\varphi\)-transforms and atomic decompositions.