 

Adam Osękowski
WeakL^{∞} inequalities for BMO functions view print


Published: 
August 4, 2015

Keywords: 
BMO, Bellman function, weaktype inequality, best constants 
Subject: 
42A05, 42B35, 49K20, 46E30. 


Abstract
Let I be an interval contained in
R and let φ:I→ R
be a given function. The paper contains the
proof of the sharp estimate
φ(1/I)∫_{I} φ_{W(I)}≦
2φ_{BMO(I)},
where W(I) is the weakL^{∞} space introduced by Bennett, DeVore and
Sharpley. The proof exploits Bellman function method: the above inequality is deduced from the existence of a special function possessing certain majorization and concavity properties.


Acknowledgements
The research was partially supported by the NCN grant DEC2012/05/B/ST1/00412.


Author information
Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02097 Warsaw, Poland
ados@mimuw.edu.pl

