On Clarkson's inequality, type and cotype for the Edmunds-Triebel logarithmic spaces

Abstract.

We show that the (p, p') Clarkson's inequality holds in the Edmunds-Triebel logarithmic spaces $A_{\theta}({\log}A)_{b,q}$ and in the Zygmund spaces $L_p({\log}L)_b(\Omega)$, for $b \in \mathbb{R}$ and for suitable $1 \leq p \leq 2$. As a consequence of these results we also obtain some new information about the types and the cotypes of these spaces.