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Parabolic sections were introduced by Huang[1] to study the parabolic Monge-Ampère equation. In this note, we introduce the generalized parabolic sections P and define BMO^q_P spaces related to these sections. We then establish the John-Nirenberg type inequality and verify that all BMO^q_P are equivalent for q ≥ 1. , number=1, journal=Analysis in Theory and Applications, year=2018, month=Aug., pages=1–9