Steklov Institute of Mathematics at St.Petersburg

PREPRINT 20/2003

THE SHARP CONSTANT IN THE JOHN-NIRENBERG INEQUALITY

This preprint was accepted December 16, 2003

ABSTRACT:
The sharp constant in the integral form of the John-Nirenberg inequality
is found by constructing of the exact Bellman function of the corresponding
extremal problem. The explicit solution of the Bellman equation is found.
Moreover, the extremal function is presented that proves sharpness of the
constant.