A geometrical/combinatorical question with implications for the John-Nirenberg inequality for BMO functions

Michael Cwikel, Yoram Sagher, and Pavel Shvartsman. "A geometrical/combinatorical question with implications for the John-Nirenberg inequality for BMO functions." Banach Center Publications 95.1 (2011): 45-53. <http://eudml.org/doc/281816>.

@article{MichaelCwikel2011,
abstract = {The first and last sections of this paper are intended for a general mathematical audience. In addition to some very brief remarks of a somewhat historical nature, we pose a rather simply formulated question in the realm of (discrete) geometry. This question has arisen in connection with a recently developed approach for studying various versions of the function space BMO. We describe that approach and the results that it gives. 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. One of our main results is that an affirmative answer to the above question would lead to a version of the John-Nirenberg inequality with "dimension free" constants.},
author = {Michael Cwikel, Yoram Sagher, Pavel Shvartsman},
journal = {Banach Center Publications},
keywords = {BMO; John-Nirenberg inequality; mean oscillation; John-Strömberg functional; ``dimension free'' inequality},
language = {eng},
number = {1},
pages = {45-53},
title = {A geometrical/combinatorical question with implications for the John-Nirenberg inequality for BMO functions},
url = {http://eudml.org/doc/281816},
volume = {95},
year = {2011},
}

TY - JOUR
AU - Michael Cwikel
AU - Yoram Sagher
AU - Pavel Shvartsman
TI - A geometrical/combinatorical question with implications for the John-Nirenberg inequality for BMO functions
JO - Banach Center Publications
PY - 2011
VL - 95
IS - 1
SP - 45
EP - 53
AB - The first and last sections of this paper are intended for a general mathematical audience. In addition to some very brief remarks of a somewhat historical nature, we pose a rather simply formulated question in the realm of (discrete) geometry. This question has arisen in connection with a recently developed approach for studying various versions of the function space BMO. We describe that approach and the results that it gives. 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. One of our main results is that an affirmative answer to the above question would lead to a version of the John-Nirenberg inequality with "dimension free" constants.
LA - eng
KW - BMO; John-Nirenberg inequality; mean oscillation; John-Strömberg functional; ``dimension free'' inequality
UR - http://eudml.org/doc/281816
ER -