Annales Academiæ Scientiarum Fennicæ

Mathematica

Volumen 45, 2020, 533-546

# A SHARP INTEGRAL INEQUALITY FOR THE DYADIC MAXIMAL OPERATOR
AND A RELATED STABILITY RESULT

## Eleftherios N. Nikolidakis

University of Ioannina, Department of Mathematics

GR 45110, Panepistimioupolis, Greece; enikolid 'at' uoi.gr

**Abstract.**
We prove a sharp integral inequality for the dyadic maximal operator due to which the evaluation of the Bellman function of this operator with respect to two variables is possible, as can be seen in [3]. Our inequality of interest is proved in this article by a simpler and more immediate way. We also study a stability result in connection with this inequality, that is we provide a necessary and sufficient condition, for a sequence of functions, under which we obtain equality in the limit. The proof of this result is based on the proof of the related inequality which we present in this article.

**2010 Mathematics Subject Classification:**
Primary 42B25.

**Key words:**
Dyadic maximal operator, Hardy type inequalities.

**Reference to this article:** E. N. Nikolidakis:
A sharp integral inequality for the dyadic maximal operator and
a related stability result.
Ann. Acad. Sci. Fenn. Math. 45 (2020), 533-546.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4517

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