Bellman function for extremal problems in BMO

@article{Ivanisvili2012BellmanFF,
  title={Bellman function for extremal problems in BMO},
  author={Paata Ivanisvili and Nikolay N. Osipov and Dmitriy M. Stolyarov and Vasily I. Vasyunin and Pavel Zatitskiy},
  journal={Transactions of the American Mathematical Society},
  year={2012},
  volume={368},
  pages={3415-3468}
}
In this paper we develop the method of nding sharp estimates by using a Bellman function. In such a form the method appears in the proofs of the classical John{Nirenberg inequality and L p estimations of BMO functions. In the present paper we elaborate a method of solving the boundary value problem for the homogeneous Monge{Amp ere equation in a parabolic strip for suciently smooth boundary conditions. In such a way, we have obtained an algorithm for constructing an exact Bellman function for a… 
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52 Citations
Background Citations
19
Methods Citations
6

52 Citations

Citation Type

Citation Type

An Example of Constructing a Bellman Function for Extremal Problems in BMO
An example of solving a boundary-value problem for a homogeneous Monge–Ampère equation is given, which produces a Bellman function for an extremal problem on the space BMO. The paper contains a…
Bellman function for extremal problems in $\mathrm{BMO}$ II: evolution
In the paper "Bellman function for extremal problems in $\mathrm{BMO}$", the authors built the Bellman function for integral functionals on the $\mathrm{BMO}$ space. The present paper provides a…
The Bellman Function for a Parametric Family of Extremal Problems in BMO
  • N. Osipov
  • Mathematics
    Journal of Mathematical Sciences
  • 2019
Let I be an interval of the real line and 〈⋅〉I be the corresponding integral average. We describe the behavior of the Bellman function for the functional F(φ) = 〈f ∘ φ〉I, φ ∈ BMO(I), as f ranges over…
A SURVEY: BELLMAN FUNCTION METHOD AND SHARP INEQUALITIES FOR MARTINGALES
Bellman function method is an efficient device which enables to relate certain types of estimates arising in probability and harmonic analysis to the existence of the associated special function…
Sharp estimates of integral functionals on classes of functions with small mean oscillation
Weak-L ∞ inequalities for BMO functions
Let I be an interval contained in R and let φ : I → R be a given function. The paper contains the proof of the sharp estimate ∣∣∣∣∣∣∣∣φ− 1 |I| ∫ I φ ∣∣∣∣∣∣∣∣ W (I) ≤ 2||φ||BMO(I), where W (I) is the…
Hessian of Bellman functions and uniqueness of the Brascamp–Lieb inequality
TLDR
Under some assumptions on the vectors a1,..,an 2 R k and the function B and thefunction B : R n ! R the authors find the sharp estimate of the expression Rk B(u1(a1 · x),...,un(an · x))dx in terms of R uj(y)dy,j = 1,...,n.
A SHARP ESTIMATE FOR MUCKENHOUPT CLASS A∞ AND BMO
A classical fact in the weighted theory asserts that a weight w belongs to the Muckenhoupt class A∞ if and only if its logarithm logw is a function of bounded mean oscillation. We prove a sharp…
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We give a characterization of the extremal sequences for the Bellman function of three variables of the dyadic maximal operator in relation to Kolmogorov's inequality. In fact we prove that they…
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