Modulus of Convexity and Inequalities of Special Martingales in Quasi-Banach Spaces

In this paper,a concept of modulus of convexity in quasi-Banach spaces,i.e.TC modulus of convexity which is an extension of that of uniform modulus of convexity is introduced and the re-quasi-normed theorem is proved.The relationships between some inequalities of special martingales with values in quasi-Banach spaces and q-uniformly TC convex quasi-Banach spaces is studied.The q-uniformly TC convex quasi-Banach spaces are characterized by inequalities of special martingales with values in quasi-Banach spaces.