Bellman Function and the $H^1-BMO$ Duality
arXiv:0809.0322
Abstract
A Bellman function approach to Fefferman's $H^1-BMO$ duality theorem is presented. One Bellman-type argument is used to handle two different one-dimensional cases, dyadic and continuous. An explicit estimate for the constant of embedding $BMO\subset (H^1)^*$ is given in the dyadic case. The same Bellman function is then used to establish a multi-dimensional analog.
14 pages, 2 figures, final version