Symmetric norms and the Leibniz property

2016/01/04 by Zoltán Léka, Leka, Zoltan
Mathematics · #15A60 #26A51 #46N30 #60A99 (Secondary) #60E15 (Primary) #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1601.00440

openalex publication_date 2016/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that certain symmetric seminorms on ℝⁿ satisfy the Leibniz inequality. As an application, we obtain that L^p norms of centered bounded real functions, defined on probability spaces, have the same property. Even though this is well-known for the standard deviation it seems that the complete result has never been established. In addition, we shall connect the results with the differential calculus introduced by Cipriani and Sauvageot and Rieffel's non-commutative Riemann metric.

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