On the John–Nirenberg inequality

[摘要] 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.

[学科分类] 电力

[关键词] BMO;John–Nirenberg inequality;Bounded mean oscillation;Dyadic decomposition