Weak integral conditions for BMO
Weak integral conditions for BMO
We study the question of how much one can weaken the defining condition of BMO. Specifically, we show that if $Q$ is a cube in $\mathbb {R}^n$ and $h:[0,\infty )\to [0,\infty )$ is such that $h(t)\to \infty$ as $t\to \infty ,$ then \[ \sup _{J~\text {subcube}~Q}\frac 1{|J|}\int _J h\big (\big …