Abstract
We give Hardy-Stein and Douglas identities for nonlinear nonlocal Sobolev-Bregman integral forms with unimodal Lévy measures. We prove that the corresponding Poisson integral defines an extension operator for the Sobolev-Bregman spaces. We also show that the Poisson integrals are quasiminimizers of the Sobolev-Bregman forms.
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