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Ufimsk. Mat. Zh., 2021, Volume 13, Issue 1, Pages 131–136 (Mi ufa551)  

On geometric properties of Morrey spaces

H. Gunawan, D. I. Hakim, A. S. Putri

Faculty of Mathematics and Natural Sciences, Jalan Ganesha No. 10, Bandung, 40132, Indonesia

Abstract: The study of Morrey spaces is motivated by many reasons. Initially, these spaces were introduced in order to understand the regularity of solutions to elliptic partial differential equations [1]. In line with this, many authors study the boundedness of various integral operators on Morrey spaces. In this article, we are interested in their geometric properties, from functional analysis point of view. We show constructively that Morrey spaces are not uniformly non-$\ell^1_n$ for any $n\ge 2$. This result is sharper than earlier results, which showed 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 $\mathcal{M}^p_q(\mathbb{R}^d)$ with $1\le p<q<\infty$ are equal to $n$.

Keywords: Morrey spaces, uniformly non-$\ell^1_n$-ness, $n$-th James constant, $n$-th Von Neumann-Jordan constant.

Funding Agency
This work is supported by P3MI-ITB 2020 Program.


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English version:
Ufa Mathematical Journal, 2021, 13:1, 131–136 (PDF, 338 kB); https://doi.org/10.13108/2021-13-1-131

Bibliographic databases:

UDC: 517.958
MSC: 46B20, 42B35
Received: 07.05.2020
Language:

Citation: H. Gunawan, D. I. Hakim, A. S. Putri, “On geometric properties of Morrey spaces”, Ufimsk. Mat. Zh., 13:1 (2021), 131–136; Ufa Math. J., 13:1 (2021), 131–136

Citation in format AMSBIB
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\paper On geometric properties of Morrey spaces
\jour Ufimsk. Mat. Zh.
\yr 2021
\vol 13
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\pages 131--136
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\vol 13
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\pages 131--136
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