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arXiv · 2003.08569

On geometric properties of Morrey spaces

Hendra Gunawan·Denny I. Hakim·Arini S. Putri
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Abstract

In this article, we show constructively that Morrey spaces are not uniformly non-$\ell^1_n$ 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 $C_{{\rm J}}^{(n)}(X)$ and the $n$-th Von Neumann-Jordan constant $C_{{\rm NJ}}^{(n)}(X)$ for a Banach space $X$, and obtain that both constants for any Morrey space $\mathcal{M}^p_q(\mathbb{R}^d)$ with $1\le p<q<\infty$ are equal to $n$.

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BibTeXRIS

Hendra Gunawan, Denny I. Hakim, Arini S. Putri. 2020-03-19. On geometric properties of Morrey spaces. https://doi.org/10.13108/2021-13-1-131

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