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arXiv · 2109.07939

Lower bound of the parabolic Hilbert commutator

Tuomas Oikari
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Abstract

Answering a key point left open in a recent work of Bongers, Guo, Li and Wick, we provide the following lower bound $$ \|b\|_{\text{BMO}_{\gamma}(\mathbb{R}^2)}\lesssim \|[b,H_{\gamma}]\|_{L^p(\mathbb{R}^2)\to L^p(\mathbb{R}^2)}, $$ where $H_{\gamma}$ is the parabolic Hilbert transform.

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Tuomas Oikari. 2021-09-16. Lower bound of the parabolic Hilbert commutator. https://doi.org/10.1016/j.aim.2022.108451

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