5 citations · 12 across the 9 of their papers we have counts for
13 papers
IDS for subordinate Brownian motions in Poisson random environment on nested fractals
Hubert Balsam, Kamil Kaleta, Mariusz Olszewski +1
We establish the Lifshitz singularity of the integrated density of states (IDS) for random Schrödinger operators \[ H^ω = ϕ(-\mathcal{L}) + V^ω \] on planar unbounded nested fracta…
Bregman variation of semimartingales
Krzysztof Bogdan, Dominik Kutek, Katarzyna Pietruska-Pałuba
We define Bregman variation of semimartingales. We give its pathwise representation, Itô-type isometry for martingales, and applications to harmonic analysis.
Polarized Hardy--Stein identity
Krzysztof Bogdan, Michał Gutowski, Katarzyna Pietruska-Pałuba
We prove the Hardy--Stein identity for vector functions in with and for the canonical paring of two real functions in …
Density of states for the Anderson model on nested fractals
Hubert Balsam, Kamil Kaleta, Mariusz Olszewski +1
We prove the existence and establish the Lifschitz singularity of the integrated density of states for certain random Hamiltonians on fractal spaces of infinite diame…
Optimal Hardy inequality for the fractional Laplacian on
Krzysztof Bogdan, Tomasz Jakubowski, Julia Lenczewska +1
For the fractional Laplacian we give Hardy inequality which is optimal in for . As an application, we explicitly characterize the contractivity of the correspondi…
Nonlinear nonlocal Douglas identity
Krzysztof Bogdan, Tomasz Grzywny, Katarzyna Pietruska-Pałuba +1
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 defin…