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Zeitschrift für Analysis und ihre Anwendungen


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Volume 14, Issue 1, 1995, pp. 105–140
DOI: 10.4171/ZAA/666

Published online: 1995-03-31

Hölder Inequalities and Sharp Embeddings in Function Spaces of $B^s_{pq}$ and $F^s_{pq}$ Type

Winfried Sickel[1] and Hans Triebel[2]

(1) Friedrich-Schiller-Universität Jena, Germany
(2) Friedrich-Schiller-Universität Jena, Germany

Besides assertions on sharp embeddings of $B^s_{pq}$ and $F^s_{pq}$ we give necessary and sufficient conditions on the parameters $s,p,q,p_1,q_1,p_2,q_2$ for the Hölder type inequalities $\| f \cdot g | B^s_{pq} \| ≤ c \| f | B^s_{p_1q_1} \| \| g | B^s_{p_2q_2}$ and $\| f \cdot g | F^s_{pq} \| ≤ c \| f | F^s_{p_1q_1} \| \| g | F^s_{p_2q_2}$ to hold.

Keywords: Function spaces, atoms, embeddings, paramultiplication, pointwise multiplication, multiplication algebras

Sickel Winfried, Triebel Hans: Hölder Inequalities and Sharp Embeddings in Function Spaces of $B^s_{pq}$ and $F^s_{pq}$ Type. Z. Anal. Anwend. 14 (1995), 105-140. doi: 10.4171/ZAA/666