Abstract
We introduce a method which can be used to establish sharp maximal estimates for functions of bounded lower oscillation (BLO). The technique allows us to deduce such estimates from the existence of certain special functions, and can be regarded as a version of Bellman function method, which has gained considerable interest in the recent literature. As an application, we establish a sharp exponential bound, which can be regarded as a version of integral John-Nirenberg inequality for BLO functions.
