Averages with the Gaussian divisor: Weighted Inequalities and the Pointwise Ergodic Theorem

2024/02/19 by Christina Giannitsi, Giannitsi, Christina, Nazar Miheisi +3
Economics, Econometrics and Finance · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2402.12457

openalex publication_date 2024/02/19 · openalex created_date 2024/02/22 · openalex updated_date 2026/07/28

Abstract

We discuss the Pointwise Ergodic Theorem for the Gaussian divisor function d(n), that is, for a measure preserving \mathbb Z[i] action T, the limit lim_{N→ ∞} (1)/(D(N)) ∑ _\mathscrN (n) ≤ N d(n) f(Tⁿ x) converges for every f∈ L^p, where \mathscrN (n) = n n, and D(N) = ∑ _\mathscrN (n) ≤ N d(n) , and 1

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