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arXiv · 2006.01932

Nonlinear nonlocal Douglas identity

Krzysztof Bogdan·Tomasz Grzywny·Katarzyna Pietruska-Pałuba·Artur Rutkowski
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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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Krzysztof Bogdan, Tomasz Grzywny, Katarzyna Pietruska-Pałuba, Artur Rutkowski. 2020-06-02. Nonlinear nonlocal Douglas identity. https://arxiv.org/abs/2006.01932

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