Nonlinear nonlocal Douglas identity

Published 2 Jun 2020 in math.AP, math.FA, and math.PR | (2006.01932v2)

Abstract: We give Hardy-Stein and Douglas identities for nonlinear nonlocal Sobolev-Bregman integral forms with unimodal L\'evy 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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