The ε-Maximal Operator and Haar Multipliers on Variable Lebesgue Spaces

2022/08/24 by David Cruz-Uribe, Cruz-Uribe, David, Michael Penrod +1
Mathematics · #42A45 #42B25 #42B35 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2208.11775

openalex publication_date 2022/08/24 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28

Abstract

C. Stockdale, P. Villarroya, and B. Wick introduced the ε-maximal operator to prove the Haar multiplier is bounded on the weighted spaces L^p(w) for a class of weights larger than A_p. We prove the ε-maximal operator and Haar multiplier are bounded on variable Lebesgue spaces \Lpp(\Rⁿ) for a larger collection of exponent functions than the log-Holder continuous functions used to prove the boundedness of the maximal operator on \Lpp(\Rⁿ). We also prove that the Haar multiplier is compact when restricted to a dyadic cube Q₀.

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