On the pointwise multiplication in Besov and Lizorkin-Triebel spaces
Let \(A^s_{pq} (\mathbb R^n)\) with \(A\in \{B,F \}\) be the nowadays well-known two scales of function spaces on \(\mathbb R^n\) where \(s \in \mathbb R\), \(0<p,q \leq \infty\). The paper deals with embedding theorems of type \[ A^{s_1}_{p_1 q_1} (\mathbb R^n) \cdot A^{s_2}_{p_2 q_2} (\mathbb R^n) \hookrightarrow A^{s_3}_{p_3 q_3} (\mathbb R^n), \] where \(A\) may be independently \(B\) or \(F\), complementing existing assertions. Of interest are borderline cases not known so far.
scientific article; zbMATH DE number 5164266