Bellman function for the Gundy theorem

We discuss how to apply the Bellman function method to general operators on martingales that are not necessarily martingale transforms. Namely, we present a Bellman-type function that gives the uniform $L^p$-boundedness for the class of operators associated with Gundy’s extrapolation theorem. As an example, we consider the operator whose $L^p$-boundedness implies Rubio de Francia's inequality for the Walsh system.
This is a joint talk with V. A. Borovitskiy and A. S. Tselishchev.