Year: 2026
Type: preprint
Abstract: We investigate two natural formulations of equal-length Littlewood--Paley--Rubio de Francia (LPR) inequalities on arbitrary Vilenkin systems \(\Gm\). The canonical formulation uses canonical intervals in \(\mathbb N\) of equal cardinality, while Vilenkin's formulation uses translates of a common initial interval under the group operation on the dual of \(\Gm\). In this paper, our main results show that the definitions of these two types of intervals exhibit dramatically different properties. More precisely, for the canonical formulation, we construct a counterexample showing that, for every \(2
Source: arXiv (Cornell University)
Authors: Chen, Deyu, Hong, Guixiang
Institution: Harbin Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G5343799843
OpenAlex ID: W7214721809