Dyadic Hardy Spaces and Bellman Function Technique

By Jingguo Lai

October 26, 2011

Abstract

The theory of classical Hardy Spaces has been well developed since 1920s, and it motivates a bunch of ideas that are extremely crucial in Harmonic analysis. Parallel to that, the theory of martingale Hardy Spaces was only sysmatically studied from early 1970s, and remains active nowadays. In this talk, I will mention some basic definitions and facts about the most simple but important version of the martingale Hardy Spaces-the Dyadic Hardy Spaces. If time permits, I will also talk about one of Sergei Treil's famous work-the Bellman Function Technique under this Dyadic Hardy Spaces setting.