Sharp results in the integral-form John-Nirenberg inequality
By L. Slavin, V. Vasyunin. 2007
116 citations recorded by the source corpus.
We consider the strong form of the John-Nirenberg inequality for the L 2 -based BMO. We construct explicit Bellman functions for the inequality in the continuous and dyadic settings and obtain the sharp constant, as well as the precise bound on the inequality's range of validity, both previously unknown. The results for the two cases are substantially different. The paper not only gives another instance in the short list of such explicit calculations, but also presents the Bellman function method as a sequence of clear steps, adaptable to a wide variety of applications.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/3a447cb60a76be02f796fadd9a7d5ca4b473734c
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In Applied Mathematics
- Alexander Volberg
- V. Vasyunin
- L. Slavin
- Nikolay N. Osipov
- Paata Ivanisvili
- D. Stolyarov
- P. Zatitskiy
- Tuomas Hytönen
Citations in the corpus
- Sharp constants in the classical weak form of the John–Nirenberg inequality (2012, methodology): “ion of the domain by the extremal lines of the solution of the Monge–Amp`re equation, the extremizers were constructed for every point of the domain. The pieces of such an approach can be found in in [8], [12], [15], [13]. The latter paper has a lengthy explanation of extremal lines of the solutions”
- Bellman function for extremal problems in BMO (2012, methodology): “It is widely known that for the John–Nirenberg inequality and for the reverse Hölder inequality for the Ap-weights, the Bellman functions can be constructed similarly (compare [12, 13, 9] and [14, 11, 7]).”
- Sharp L^p estimates on BMO (2011, methodology): “s (2.1) 1 k’k 2 1 k ’k C(k’k) 1 k’k 2 2 1 k ’k : By \sharp" we mean that there exist functions ’ with norm 1 for which the inequality fails. The reader can compare this result with the one in [SV], where the sharp one-sided John{Nirenberg inequality was proved. One can get a sub-optimal two-si”