  We discuss the dyadic John-Nirenberg space that is a generalization of
functions of bounded mean oscillation. A John-Nirenberg inequality, which gives
a weak type estimate for the oscillation of a function, is discussed in the
setting of medians instead of integral averages. We show that the dyadic
maximal operator is bounded on the dyadic John-Nirenberg space and provide a
method to construct nontrivial functions in the dyadic John-Nirenberg space.
Moreover, we prove that the John-Nirenberg space is complete. Several open
problems are also discussed.
