This is an announcement for the paper "Uchiyama's lemma and the John-Nirenberg inequality" by Greg Knese. Abstract: Using integral formulas based on Green's theorem and in particular a lemma of Uchiyama, we give simple proofs of comparisons of different BMO norms without using the John-Nirenberg inequality while we also give a simple proof of the strong John-Nirenberg inequality. Along the way we prove the inclusions of BMOA in the dual of H^1 and BMO in the dual of real H^1. Archive classification: math.CV math.FA Mathematics Subject Classification: 30H35, 30H10, 30J99 Remarks: 13 pages Submitted from: geknese@bama.ua.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1201.5354 or http://arXiv.org/abs/1201.5354