Hausdorff Measures and Functions of Bounded Quadratic Variation

2009/03/16 by Dimitris Apatsidis, Spiros A. Argyros, Apatsidis, D. +3
Mathematics · #28A78 #46B20 #46B26 #Advanced Harmonic Analysis Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.0903.2809

openalex publication_date 2009/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To each function f of bounded quadratic variation (f∈ V₂) we associate a Hausdorff measure μ_f. We show that the map f→μ_f is locally Lipschitz and onto the positive cone of M[0,1]. We use the measures \μ_f:f∈ V₂\ to determine the structure of the subspaces of V₂⁰ which either contain c₀ or the square stopping time space S².

Citations

• An inequality of the Hölder type, connected with Stieltjes integration

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