Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 889-904

BEST CONSTANTS IN MUCKENHOUPT'S INEQUALITY

Adam Osekowski

University of Warsaw, Department of Mathematics, Informatics and Mechanics
Banacha 2, 02-097 Warsaw, Poland; ados 'at' mimuw.edu.pl

Abstract. The paper identifies optimal constants in weighted L^p inequalities for the dyadic maximal function. The proof rests on Bellman function technique: the estimates are deduced from the existence of certain special functions enjoying appropriate size conditions and concavity.

2010 Mathematics Subject Classification: Primary 42B25; Secondary 46E30, 60G42.

Key words: Maximal, dyadic, Bellman function, best constants.

Reference to this article: A. Osekowski: Best constants in Muckenhoupt's inequality. Ann. Acad. Sci. Fenn. Math. 42 (2017), 889-904.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4256