BMO Spaces Associated to Generalized Parabolic Sections

Abstract

Parabolic sections were introduced by Huang^[1] to study the parabolic Monge-Ampère equation. In this note, we introduce the generalized parabolic sections $\mathcal{P}$ and define $BMO^q_{\mathcal{P}}$ spaces related to these sections. We then establish the John-Nirenberg type inequality and verify that all $BMO^q_{\mathcal{P}}$ are equivalent for $q \geq 1.$