Representation theorems for functions of vanishing mean oscillation

2023/09/12 by Lu, Zheng-yi, Tao, Fei, Yang, Yaosong
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.06155

Abstract

As a significant application of the duality theory between real Hardy spaces H¹(ℝⁿ) and BMO(ℝⁿ), Fefferman and Stein developed a representation theorem for BMO(ℝⁿ) by utilizing the Riesz transforms (n≥ 1). L. Carleson provided a constructive proof for the case n=1. In this article, we propose a representation theorem for VMO(\mathbbS) using Carleson's construction and demonstrate a representation theorem for VMO(ℝⁿ) through an iterative process. Additionally, we provide a brand-new characterization of VMO as an application of our results.

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