New York Journal of Mathematics
Volume 21 (2015) 699-713


Adam Osękowski

Weak-L inequalities for BMO functions

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Published: August 4, 2015
Keywords: BMO, Bellman function, weak-type inequality, best constants
Subject: 42A05, 42B35, 49K20, 46E30.

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)≦ 2||φ||BMO(I),
where W(I) is the weak-L 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.


The research was partially supported by the NCN grant DEC-2012/05/B/ST1/00412.

Author information

Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland