  This paper investigates the concept of harmonic functions of bounded mean
oscillation, starting from John-Nirenberg's pioneering studies, under a renewed
formalism, suitable for bringing out some fundamental properties inherent in
it. In more detail: after a quick introduction, the second Section presents the
main theorem, plus complete proof, relating to this function; in the third
Section there is a suggestion on the exponential integrability (theorem and
sketch of proof), while the fourth Section deals with the duality of Hardy
Space $H^1$ and bounded mean oscillation, with some ideas for a demonstration.
The writing closes with a graphic appendix.
