On the John–Nirenberg inequality

Abstract

Abstract We present a version of the John–Nirenberg inequality for a sub-class of BMO by estimating the corresponding mean oscillating distribution function via dyadic decomposition. The dominating functions are of the form of decreasing step functions which are finer than the classical exponential functions and might be much more efficient for some sophisticated analysis. We also prove that the modified BMO-norm is equivalent to the classical BMO-norm under the convexity assumption.

Keywords

• BMO
• John–Nirenberg inequality
• Bounded mean oscillation
• Dyadic decomposition