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arXiv · 1411.5408

The Bellman functions of the Carleson Embedding Theorem and the Doob's martingale inequality

Jingguo Lai
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Abstract

Evaluation of the Bellman functions is a difficult task. The exact Bellman functions of the dyadic Carleson Embedding Theorem 1.1 and the dyadic maximal operators are obtained in [3] and [4]. Actually, the same Bellman functions also work for the tree-like structure. In this paper, we give a self-complete proof of the coincidence of the Bellman functions on the more general infinitely refining filtered probability space, see Definition 1.3. The proof depends on a remodeling of the Bellman function of the dyadic Carleson Embedding Theorem.

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Jingguo Lai. 2015-02-11. The Bellman functions of the Carleson Embedding Theorem and the Doob's martingale inequality. https://arxiv.org/abs/1411.5408

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