Analytic Q-uniform Convexity Of Complex Quasi Banach Space And Atomic Decomposition Of Hardy Martingales

As a useful tool,the atomic decomposition method plays an important part in harmonicanalysis and martingale theory.By the atomic decomposition of martingale,we can establish therelationships between martingale spaces.To martingales with Banach-space value,the results aretightly related to the geometry properties and structure of the spaces in which the martingalestake value.In this paper,we study the atomic decomposition of Hardy martingales with values incomplex quasi-Banach space and discuss the embedding relationships between Hardy martin-gale spaces.The results characterize the analytic q-uniform convexity of complex quasi-Banachspace.This thesis consists of three chapters. In chapter 1,the history of martingale spaces the-ory and atomic method is introduced.In chapter 2,some basic conceptions are described, suchas martingale,stopping time,atom,Hardy martingale,analytic q-uniform convexity,and so on.Inchapter 3,we establish several theorems about the atomic decomposition of Hardy martingalewith value in complex quasi-Banach space and characterize the analytic q-uniform convexityof complex quasi-Banach space.The embedding relationships between two Hardy martingalespaces is given at the end of chapter 3.