Uniformly Convexity Of Complex Spaces And Weak Orlicz Space Norm Inequalities Of Martingale

This paper contains two chapters,the outline of the paper is arranged as follows:In chapter l,we introduce the background and summarily describe the basic knowledge needed in the followings.In chapter 2,we generalize some results in[4] to weak Orlicz space.That is, we discuss the analytic q-uniformly convexity of complex quasi-Banach space,using weak Orlicz space norm inequalities of Hardy martingales with values in it give characterisations of this convexity.Similarly,we also generalize some results in[7] to weak Orlicz space.That is,we dis-cuss q-uniformly PL-convexity of complex quasi-Banach space,using weak Orlicz space norm inequalities of analytic martingales with values in it give characterisations of this convexity.