A new look at the John-Nirenberg and John-Stromberg theorems for BMO. Lecture Notes

Details A new look at the John-Nirenberg and John-Stromberg theorems for BMO. Lecture Notes A new look at the John-Nirenberg and John-Stromberg theorems for BMO. Lecture Notes

2010-11-02

arxiv.org/abs/1011.0766v1

Mathematics

Functional Analysis

64 pages. Section 11 (on pages 55-63) consists of several appendices containing material which will be already well known to m

Scientific paper

We develop some techniques for studying various versions of the function space BMO. Special cases of one of our results give alternative proofs of the celebrated John- Nirenberg inequality and of related inequalities due to John and to Wik. Our approach enables us to pose a simply formulated "geometric" question, for which an affirmative answer would lead to a version of the John-Nirenberg inequality with dimension free constants. A more detailed summary of the main ideas and results of this paper can be found at http://www.math.technion.ac.il/~mcwikel/bmo/CwikSaghShvaSummary.pdf

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