Lower bound of the parabolic Hilbert commutator

Abstract

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

V1: 26 pages, 2 figures. V2: References and funding information updated

References in corpus (4)

• On the Hardy space theory of compensated compactness quantities
• Off-diagonal estimates for bi-commutators
• The unified theory for the necessity of bounded commutators and applications
• Off-diagonal estimates for bilinear commutators