Sharp estimates of integral functionals on classes of functions with small mean oscillation

DOI10.1016/j.crma.2015.07.016zbMath1338.42031arXiv1412.4749OpenAlexW2963529531MaRDI QIDQ5965088

Nikolay N. Osipov, Paata Ivanisvili, Pavel B. Zatitskiy, Dmitriy M. Stolyarov, Vasily I. Vasyunin

Publication date: 2 March 2016

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.4749

zbMATH Keywords

integral functionalsBMO spaceBellman function problemsGehring classMuckenhoupt classsmall mean oscillation

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Harmonic analysis in several variables (42B99)

Related Items (10)

Theory of locally concave functions and its applications to sharp estimates of integral functionals ⋮ Hessian of Bellman functions and uniqueness of the Brascamp–Lieb inequality ⋮ The John–Nirenberg constant of $\mathrm {BMO}^p$, $p> 2$ ⋮ Sharp multiplicative inequalities with BMO I ⋮ Bellman Function for Extremal Problems in BMO II: Evolution ⋮ Sharpening Hölder's inequality ⋮ Sharp transference principle for BMO and \(A_p\) ⋮ Monotonic rearrangements of functions with small mean oscillation ⋮ Burkholder meets Gundy: Bellman function method for general operators on martingales ⋮ Dimension-free estimates for semigroup BMO and A_p

Cites Work

• On Bellman function for extremal problems in BMO
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• Monge-Ampère equations and Bellman functions: the dyadic maximal operator
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• The exact continuation of a reverse Hölder inequality and Muckenhoupt's conditions
• Sharp weak type estimates for weights in the class \(A_{p_1, p_2}\)
• Sharp inequalities for BMO functions
• Theory of locally concave functions and its applications to sharp estimates of integral functionals
• Bellman VS. Beurling: sharp estimates of uniform convexity for $L^p$ spaces
• Some Applications of Equimeasurable Rearrangements
• Sharp L^p estimates on BMO
• Sharp results in the integral-form John–Nirenberg inequality
• The sharp constant in the reverse Hölder inequality for Muckenhoupt weights
• Weak integral conditions for BMO
• Sharp estimates involving $A_\infty $ and $L\log L$ constants, and their applications to PDE
• The Bellman functions for a certain two-weight inequality: A case study
• Monge--Amp\`ere equation and Bellman optimization of Carleson Embedding Theorems
• Sharp constants in the classical weak form of the John-Nirenberg inequality

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