Maximal operator in Musielak--Orlicz--Sobolev spaces

2023/03/29 by Piotr Michał Bies, Bies, Piotr Michał, Michał Gaczkowski +3
Mathematics · #42B25 #46E35 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2303.16587

openalex publication_date 2023/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Hardy-Littlewood maximal operator in the Musielak-Orlicz-Sobolev space W^1,φ(ℝⁿ). Under some natural assumptions on φ we show that the maximal function is bounded and continuous in W^1,φ(ℝⁿ).

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