Paata Ivanisvili

Hessian of Bellman functions and uniqueness of the Brascamp–Lieb inequality

Under some assumptions on the vectors a1,..,an 2 R k and the function B : R n ! R we find the sharp estimate of the expressionRk B(u1(a1 · x),...,un(an · x))dx in terms ofR uj(y)dy,j = 1,...,n. In some particular case we will show that these assumptions on B imply that there is only one Brascamp-Lieb inequality.

Inequality for Burkholder’s martingale transform

We find the sharp constant

Isoperimetric functional inequalities via the maximum principle: The exterior differential systems approach

C=C(\tau,p, \mathbb{E}G, \mathbb{E}F)

Improving Beckner’s bound via Hermite functions

of the following inequality

Square functions and the Hamming cube: duality

\|(G^{2}+ \tau^{2} F^{2})^{1/2} \|_{p} \leq C \|F\|_{p},

BELLMAN FUNCTION APPROACH TO THE SHARP CONSTANTS IN UNIFORM CONVEXITY

where

Bellman function for extremal problems in BMO

G

Bellman VS. Beurling: sharp estimates of uniform convexity for ^{} spaces

is the transform of a martingale

Bellman partial differential equation and the hill property for classical isoperimetric problems

F

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

under a predictable sequence