Smoothness spaces related to Morrey spaces – a survey. I
We discuss different strategies to introduce smoothness spaces related to Morrey spaces. In particular, we consider the Nikol’skij-Besov type spaces \( B^s,τ_p,q \) and the Lizorkin-Triebel type spaces \( F^s,τ_p,q \), and compare them with other possibilities of defining smoothness spaces of Nikol’skij–Besov–Lizorkin–Triebel type related to Morrey spaces. Altogether we discuss eight scales of function spaces: \( B^s,τ_p,q \), \( F^s,τ_p,q \), \( N^s_p,q,u \), \( E^s_p,q,u \), \( B^s,τ_p,q,unif \), and \( F^s,τ_p,q,unif \). Differences between the scales \( B^s,τ_p,q \) and \( N^s_p,q,u \) (for \( q<∞ \)) are discussed in detail. , number=3, journal=Eurasian Mathematical Journal, author=Sickel, W., year=2012, month=Oct., pages=110–149