Variable Muckenhoupt weights with applications in approximation

2021/09/01 by Ramazam Akgün, Akgün, Ramazam
Mathematics · #41A28 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Approximation and Integration #Primary 42A10 #Secondary 41A17

paper · pdf · doi:10.48550/arxiv.2109.00290

openalex publication_date 2021/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Variable Muckenhoupt weights are considered in variable exponent Lebesgue spaces. Applications are given for polynomial approximation in these spaces. Boundedness of averaging operator is proved to gain a transference result. Almost all weighted norm inequalities are obtained using this transference result. Potential type approximate identities are considered. Translations of Steklov operator are proved to be bounded in these spaces. K-functional is a good apparatus for measuring smoothness properties of functions given in these function classes. Main inequalities of approximation are derived.

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