On geometric properties of Morrey spaces

Abstract

In this article, we show constructively that Morrey spaces are not uniformly non-${\ell }_n^1$ for any $n\ge 2$. This result is sharper than those previously obtained in \cite{GKSS, MG}, which show that Morrey spaces are not uniformly non-square and also not uniformly non-octahedral. We also discuss the $n$-th James constant $C_{\mathrm{J}}^{(n)}(X)$ and the $n$-th Von Neumann-Jordan constant $C_{\mathrm{NJ}}^{(n)}(X)$ for a Banach space $X$, and obtain that both constants for any Morrey space ${\mathcal{M}}_q^p({\mathbb{R}}^d)$ with $1\le p<q<\infty$ are equal to $n$.

5 pages

References in corpus (1)

• On geometric constants for (small) Morrey spaces