In this paper, we consider a non-smooth atomic decomposition by using a smooth atomic decomposition. Applying the non-smooth atomic decomposition, a local means characterization and a quarkonical decomposition, we obtain a pointwise multiplier and a trace operator for generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on the whole space. We also develop the theory of those spaces on domains. We consider an extension operator and a trace operator on the upper half space and on compact oriented Riemannian manifolds.
- Besov space
- Morrey space
- Primary: 42B35; Secondary: 41A17
- Triebel–Lizorkin space
- non-smooth atomic decomposition
- trace operator
ASJC Scopus subject areas