On the exactness of the conditions of embedding theorems for spaces of functions with mixed logarithmic smoothness

2023/08/16 by Г. Акишев, Akishev, Gabdolla
Mathematics · #41A10 and 41A25 #42A05 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Approximation and Integration #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2308.08338

openalex publication_date 2023/08/16 · openalex created_date 2023/08/18 · openalex updated_date 2026/07/28

Abstract

The article considers the Lorentz space L_p,τ(\mathbbT^m), 2π of periodic functions of many variables and S_p,τ,θ^0, bB, S_{p, τ, θ}^0, bB -- spaces of functions with mixed logarithmic smoothness. The article establishes necessary and sufficient conditions for embedding the spaces S_{p, τ, θ}^0, bB and S_{p, τ, θ}^ 0, bB into each other.

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