Abstract
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 large class of integral functionals on the BMO space.
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