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.
Highlights
1 Introduction The space of functions of bounded mean oscillation(BMO) first appeared in the work of John and Nirenberg [1] in the context of nonlinear partial differential equations that arise in the study of minimal surfaces
The space BMO can be characterized by the form of the John–Nirenberg inequality: it says that for f ∈ BMO, one has
We present a dominating function F that is finer than the exponential functions at the right-hand side of estimate
Summary
The space of functions of bounded mean oscillation(BMO) first appeared in the work of John and Nirenberg [1] in the context of nonlinear partial differential equations that arise in the study of minimal surfaces. The space BMO can be characterized by the form of the John–Nirenberg inequality: it says that for f ∈ BMO, one has 1 |Q|
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