Leonid Slavin

Sharp results in the integral-form John-Nirenberg inequality

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 inequalitys 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.

Weak integral conditions for BMO

We study the question of how much one can weaken the defining condition of BMO. Specifically, we show that if

Monge-Ampère equations and Bellman functions : The dyadic maximal operator

Q

Sharp L^p estimates on BMO

is a cube in

Bellman Function and the

\mathbb{R}^n

H^1-BMO

and

Duality

h:[0,\infty)\to[0,\infty)

NEW ESTIMATES FOR THE BEURLING-AHLFORS OPERATOR ON DIFFERENTIAL FORMS

is such that

Best constants for a family of Carleson sequences

h(t)\underset{t\to\infty}{\longrightarrow}\infty,

The John--Nirenberg constant of

then