Nonlinear nonlocal Douglas identity
Krzysztof Bogdan, Tomasz Grzywny, Katarzyna Pietruska-Pa{\l}uba, and, Artur Rutkowski
TL;DR
This paper develops Hardy-Stein and Douglas identities for nonlinear nonlocal Sobolev-Bregman forms with unimodal Lévy measures, establishing the Poisson integral as an extension operator and quasiminimizer.
Contribution
It introduces new identities and properties for nonlinear nonlocal Sobolev-Bregman spaces involving Lévy measures, expanding theoretical understanding.
Findings
Poisson integral acts as an extension operator for Sobolev-Bregman spaces
Poisson integrals are quasiminimizers of Sobolev-Bregman forms
Establishes Hardy-Stein and Douglas identities in this context
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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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Mathematical Physics Problems · Geometric Analysis and Curvature Flows