2017/03/16 by Ciqiang Zhuo, Dachun Yang, Zhuo, Ciqiang +3
Computer Science · Mathematics · #46B70 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Numerical methods in inverse problems #Primary 42B30 #Secondary 42B35
paper · pdf · doi:10.48550/arxiv.1703.05527
openalex publication_date 2017/03/16 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
Let p(⋅): \mathbb Rn→(0,∞) be a variable exponent function satisfying the globally log-Hölder continuous condition. In this article, the authors first obtain a decomposition for any distribution of the variable weak Hardy space into "good" and "bad" parts and then prove the following real interpolation theorem between the variable Hardy space Hp(⋅)(\mathbb Rn) and the space L∞(\mathbb Rn): (Hp(⋅)(\mathbb Rn),L∞(\mathbb Rn))θ,∞ =W Hp(⋅)/(1-θ)(\mathbb Rn), θ∈(0,1), where W Hp(⋅)/(1-θ)(\mathbb Rn) denotes the variable weak Hardy space. As an application, the variable weak Hardy space W Hp(⋅)(\mathbb Rn) with p-:=\mathopess infx∈\rnp(x)∈(1,∞) is proved to coincide with the variable Lebesgue space W Lp(⋅)(\mathbb Rn).