A note on Boussinesq maximal estimate

Abstract

We considered the Boussinesq maximal estimate when $ n\geq1 $. We obtained the Boussinesq maximal operator $ \mathcal{B}_E^\ast f $ is bounded from $ L^2(\mathbb{R}^n) $ to $ L^2(\mathbb{R}^n) $ when $ f\in L^2(\mathbb{R}^n) $ and $ \text{supp}\; \hat f\subset B(0, \lambda) $.

Keywords

• boussinesq operator
• maximal estimate
• bounded
• frequency decomposition
• linearization