New Bellman induction and a weak version of $\mathrm{BMO}$
Egor Dobronravov, Dmitriy Mikhailovich Stolyarov, Pavel B. Zatitskiy · arXiv (Cornell University) · 2024
We enlarge the area of applicability of the Bellman function method to estimates in the spirit of the John--Nirenberg inequality abandoning certain convexity assumptions. As an application, we consider a characteristic of a function that is much smaller than the $\mathrm{BMO}$ norm, but whose finiteness leads to the exponential integrability of the function.