Isosceles Orthogonal Geometric Constants for Morrey Spaces

Abstract

In this paper, we calculate the value of new geometric constants for the Morrey spaces and small Morrey spaces. The new geometric constants which were investigated are generalizations of the other new constants $\Omega(X)$ and $\overline{\Omega}(X)$ for Banach spaces $X$. The two constants are related to isosceles orthogonal type and introduced by Liu \textit{et al} in 2022. We introduce the generalizations of the constants which are denoted by $\Omega^{(s)}(X)$ and $\overline{\Omega}^{(s)}(X)$ for $s \geq 1$. We calculate the value of each of the constants for Morrey spaces $\mathcal{M}_q^p$ and small Morrey spaces $m_{q,\lambda}^p$. The results show that $\Omega^{(s)}(\mathcal{M}_q^p) = \frac{2^{s+1}}{5^{s-1}}$ and $\overline{\Omega}^{(s)}(m_{q,\lambda}^p) = \frac{2^{s+1}}{5^{s-1}}.$

Keywords

• Geometric constants
• isosceles orthogonal
• Morrey spaces
• small Morrey spaces.

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