There is no local unconditional structure in anisotropic spaces of smooth functions

DOI10.1007/BF00969647zbMath0711.46021MaRDI QIDQ923317

N. G. Sidorenko, Sergei V.Kislyakov

Publication date: 1988

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

local unconditional structureanisotropic space of smooth functionsBanach space of all continuous functions on the toruscontinuous derivatives

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Classical Banach spaces in the general theory (46B25) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Banach spaces of continuous, differentiable or analytic functions (46E15)

Related Items (2)

Absence of local unconditional structure in spaces of smooth functions on two-dimensional torus ⋮ Absence of local unconditional structure in spaces of smooth functions on the torus of arbitrary dimension

Cites Work

• Nonisomorphy of certain Banach spaces of smooth functions to the space of continuous functions
• Absolutely summing operators and local unconditional structures
• Sobolev imbedding operators and the nonisomorphism of certain Banach spaces
• Inequalities for functions of the classes \(W^{\overrightarrow{m}}_p(R^n)\)
• Absolutely summing operators and translation invariant spaces of functions on compact abelian groups
• Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach
• Singular integrals with mixed homogeneity
• IMPOSSIBILITY OF A UNIFORM HOMEOMORPHISM BETWEEN SPACES OF SMOOTH FUNCTIONS OF ONE AND OF $ n$ VARIABLES $ (n\geq2)$
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