Nonlinear nonlocal Douglas identity

Abstract We give Hardy–Stein and Douglas identities for nonlinear nonlocal Sobolev–Bregman integral forms with unimodal Lévy measures. prove that the corresponding Poisson defines an extension operator spaces. As application, we obtain boundedness of Dirichlet-to-Neumann on weighted $$L^p$$ L p also show integrals are quasiminimizers forms.