In this paper we prove Hölder inequalities for the Besov-Morrey spaces Nu,p,qs(Rd) and the Triebel-Lizorkin-Morrey spaces Eu,p,qs(Rd)
Nearby in the stack
. We observe that these Morrey smoothness spaces are pointwise multiplier spaces if certain conditions concerning the parameters also including
s>dmax(0,p1−1)
are fulfilled. In this context we significantly generalize the Hölder inequalities for the original Besov and Triebel-Lizorkin spaces obtained by Sickel and Triebel in 1995. For the proofs we use paramultiplication and some Franke-Jawerth embeddings obtained by Haroske and Skrzypczak.