Dynamically consistent nonlinear evaluations with their generating functions in L p

In this paper, we study dynamically consistent nonlinear evaluations in L ^p (1 < p < 2). One of our aim is to obtain the following result: under a domination condition, an F _t -consistent evaluation is an E ^g -evaluation in L ^p . Furthermore, without the assumption that the generating function g (t, ω, y, z) is continuous with respect to t, we provide some useful characterizations of an E ^g -evaluation by g and give some applications. These results include and extend some existing results.