Random Power Series in Qp, 0 Spaces. (4th October 2021)

• Record Type: Journal Article
• Authors: Li, Haiyin; Wu, Yan
• Other Names: Lastra Alberto Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-10-04
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/1449080
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Aulaskari et al. proved if 0 < p < 1 and ε n is sequence of independent, identically distributed Rademacher random variables on a probability space, then the condition Σ n = 0 ∞ n 1 − p a n 2 < ∞ implies that the random power series R f z = ∑ n = 0 ∞ a n ε n z n ∈ Q p almost surely. In this paper, we improve this result showing that the condition Σ n = 0 ∞ n 1 − p a n 2 < ∞ actually implies R f ∈ Q p, 0 almost surely.