On Some Properties of Superreflexive Besov Spaces

Autor: A. N. Agadzhanov
Rok vydání: 2020
Předmět:
Zdroj: Doklady Mathematics. 101:177-181
ISSN: 1531-8362
1064-5624
DOI: 10.1134/s1064562420030035
Popis: This paper contains results concerning superreflective Besov spaces $$B_{{p,q}}^{s}({{\mathbb{R}}^{n}})$$ . 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 $$B_{{p,q}}^{s}({{\mathbb{R}}^{n}})$$ 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 $$B_{{p,q}}^{s}({{\mathbb{R}}^{n}})$$ can be obtained in terms of the expansion coefficients of these elements in unconditional normalized Schauder bases.
Databáze: OpenAIRE
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