2024/02/01 by Jiale Chen, Xin Guo, Chen, Jiale +3
Mathematics · #30B50 #30H20 #46E15 #47H30 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2402.00314
openalex publication_date 2024/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we completely give the solution of the problem of Littlewood-type randomization in the Hardy and Bergman spaces of Dirichlet series. The Littlewood-type theorem for Bergman spaces of Dirichlet series is very different from the corresponding version for Hardy spaces of Dirichlet series; but also exhibits various pathological phenomena compared with the setting of analytic Bergman spaces over the unit disk, due to the fact that Dirichlet series behave as power series of infinitely many variables. A description for the inclusion between some mixed norm spaces of Dirichlet series plays an essential role in our investigation. Finally, as another application of the inclusion, we completely characterize the superposition operators between Bergman spaces of Dirichlet series.