Biparameter BMO under the action of a rotation

2020/10/16 by Frédéric Bernicot, Bernicot, Frédéric, Yujia Zhai +1
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #math.CA

paper · pdf · doi:10.48550/arxiv.2010.08448

arxiv created 2020/10/16 · openalex publication_date 2020/10/16 · arxiv updated 2020/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we aim to study the action of composing by a rotation on the biparameter BMO space in ℝ². This BMO space is not preserved by a rotation since it relies on the structure of axis-parallel rectangles. We will quantify this fact by interpolation inequalities. One straightforward application of the interpolation inequalities is a boundedness property of directional Hilbert transforms.

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