A necessary condition for the boundedness of the maximal operator on L^p(⋅) over reverse doubling spaces of homogeneous type

2024/03/16 by Oleksiy Karlovych, Karlovych, Oleksiy, Alina Shalukhina +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2403.10915

openalex publication_date 2024/03/16 · openalex created_date 2024/03/21 · openalex updated_date 2026/07/28

Abstract

Let (X,d,μ) be a space of homogeneous type and p(⋅):X→[1,∞] be a variable exponent. We show that if the measure μ is Borel-semiregular and reverse doubling, then the condition \rm ess inf_{x∈ X}p(x)>1 is necessary for the boundedness of the Hardy-Littlewood maximal operator M on the variable Lebesgue space L^p(⋅)(X,d,μ).

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