Geodesic
On some properties of superreflexive Besov spaces
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 5-10

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This paper contains results concerning superreflective Besov spaces $B^s_{p,q}(\mathbb{R}^n)$. Namely, expressions for convexity moduli and smoothness moduli with respect to the “canonical” norms are derived, and properties related to the finite representability of Banach spaces and linear compact operators in $B^s_{p,q}(\mathbb{R}^n)$ are examined. Additionally, inequalities of the Prus–Smarzewski type for arbitrary equivalent norms and inequalities of the James–Gurariy type are presented. Based on the latter, two-sided estimates for the norms of elements in $B^s_{p,q}(\mathbb{R}^n)$ can be obtained in terms of the expansion coefficients of these elements in unconditional normalized Schauder bases.
Keywords: superreflexivity, finite representability, Besov spaces, convexity moduli, smoothness moduli. 
@article{DANMA_2020_492_a0,
     author = {A. N. Agadzhanov},
     title = {On some properties of superreflexive {Besov} spaces},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {5--10},
     publisher = {mathdoc},
     volume = {492},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_492_a0/}
}
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A. N. Agadzhanov. On some properties of superreflexive Besov spaces. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 5-10. http://geodesic.mathdoc.fr/item/DANMA_2020_492_a0/