论文标题
关于莫雷空间的几何特性
On geometric properties of Morrey spaces
论文作者
论文摘要
在本文中，我们建设性地表明，对于任何$ n \ ge 2 $，Morrey空间不是均匀的 - $ \ ell^1_n $。该结果比以前在\ cite {gkss，mg}中获得的结果更清晰，后者表明莫雷空间不是统一的非方面，也不是统一的非二十六角体。我们还讨论了$ n $ -th James Constant $ c _ {\ rm j}^{（n）}（x）$和$ n $ -th von neumann-jordan constant $ c _ {\ rm nj}^{（n）}（x）（x）（x）$ for Banach Space $ x $，并获取该莫尔的任何Morre x $ $ \ MATHCAL {M}^p_q（\ Mathbb {r}^d）$，$ 1 \ le P <q <q <\ infty $等于$ n $。
In this article, we show constructively that Morrey spaces are not uniformly non-$\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 $n$.
