Atomic Decompositions Of Martingale Orlicz-Hardy Spaces

The main purpose of this thesis is to summarize and extend the atomic decompositions of martingale Orlicz-Hardy spaces, we prove the atomic decompositions theorem in vector-valued martingale Orlicz-Hardy spaces with Φ function properties, these results are in close contact with the geometric properties of Banach spaces. On the one hand, we extend the atomic decompositions in Hardy spaces to Orlicz-Hardy spaces; on the other hand, we extend the atomic decompositions in the scalar-valued Orlicz-Hardy spaces to the vector-valued Orlicz-Hardy spaces. This thesis is constructed as follows:In Chapter1we introduce the background and the main work of this thesis briefly.In Chapter2we introduce some notations and properties about martingale spaces and Φ function, then give some definitions of several atoms and some lemma we will use.In Chapter3we summarize the existing results of atomic decompositions in the vector-valued Hardy spaces and the scalar-valued Orlicz-Hardy spaces.Chapter4is the main content section. We obtain the atomic decompositions in the vector-valued Orlicz-Hardy spaces, which extend the results of Chapter3.