The equivalence of two conditions for weight functions for martingales (Q1892969)

In the framework of real analysis, Muckenhoupt has given a condition for weights which is equivalent to the \(A_ \infty\) condition. The authors state an analogue condition in the setting of continuous martingales, and prove that it is still equivalent to the \(A_ \infty\) condition for martingales. An application is given to some weighted norm inequality.