An eigenfunction stability estimate for approximate extremals of the Bellman function for the dyadic maximal operator on $L^{p}$
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- by Antonios D. Melas PDF
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Abstract:
We prove a stability estimate for the functions that are almost extremals for the Bellman function related to the $L^{p}$ norm of the dyadic maximal operator in the case $p\geq 2$. This estimate gives that such almost extremals are also almost âeigenfunctionsâ for the dyadic maximal operator, in the sense that the $L^{p}$ distance between the maximal operator applied to the function and a certain multiple of the function is small.References
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Additional Information
- Antonios D. Melas
- Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis 15784, Athens, Greece
- MR Author ID: 311078
- Email: amelas@math.uoa.gr
- Received by editor(s): April 9, 2014
- Published electronically: April 18, 2019
- Additional Notes: This research has been co-financed by the European Union and Greek national funds through the Operational Program âEducation and Lifelong Learningâ of the National Strategic Reference Framework (NSRF). ARISTEIA I, MAXBELLMAN 2760, research number 70/3/11913
- Communicated by: Alexander Iosevich
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3367-3375
- MSC (2010): Primary 42B25
- DOI: https://doi.org/10.1090/proc12740
- MathSciNet review: 3981115