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arXiv · 2010.08448

Biparameter $\text{BMO}$ under the action of a rotation

Frédéric Bernicot·Yujia Zhai
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Abstract

In this work, we aim to study the action of composing by a rotation on the biparameter $\text{BMO}$ space in $\mathbb{R}^2$. This $\text{BMO}$ 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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Frédéric Bernicot, Yujia Zhai. 2020-10-16. Biparameter $\text{BMO}$ under the action of a rotation. https://arxiv.org/abs/2010.08448

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