11 citations · 28 across the 16 of their papers we have counts for
20 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…
Lifshitz tail for continuous Anderson models driven by Lévy operators
Kamil Kaleta, Katarzyna Pietruska-Pałuba
We investigate the behavior near zero of the integrated density of states for random Schrödinger operators in , , where is a co…
Lifschitz tail for alloy-type models driven by the fractional Laplacian
Kamil Kaleta, Katarzyna Pietruska-Pałuba
We establish precise asymptotics near zero of the integrated density of states for the random Schrödinger operators in for the full range of $…
Reflected Brownian motion on simple nested fractals
Kamil Kaleta, Mariusz Olszewski, Katarzyna Pietruska-Pałuba
We prove the existence of the reflected diffusion on a complex of an arbitrary size for a large class of planar simple nested fractals. Such a process is obtained as a folding proj…
Extension and trace for nonlocal operators
Krzysztof Bogdan, Tomasz Grzywny, Katarzyna Pietruska-Pałuba +1
We prove an optimal extension and trace theorem for Sobolev spaces of nonlocal operators. The extension is given by a suitable Poisson integral and solves the corresponding nonloca…
The quenched asymptotics for nonlocal Schrödinger operators with Poissonian potentials
Kamil Kaleta, Katarzyna Pietruska-Pałuba
We study the quenched long time behaviour of the survival probability up to time , of a symmetric Lévy process with jumps…
Lifschitz singularity for subordinate Brownian motions in presence of the Poissonian potential on the Sierpiński gasket
Kamil Kaleta, Katarzyna Pietruska-Pałuba
We establish the Lifschitz-type singularity around the bottom of the spectrum for the integrated density of states for a class of subordinate Brownian motions in presence of the no…
Lifschitz tail and sausage asymptotics for stable processes in the Poissonian environment on the Sierpinski gasket
Dorota Kowalska, Katarzyna Pietruska-Pałuba
We obtain the Lifschitz tail asymptotics for the integrated density of states of the subordinate stable processes on the Sierpiński gasket evolving among killing…
Integrated density of states for Poisson-Schrödinger perturbations of subordinate Brownian motions on the Sierpiński gasket
Kamil Kaleta, Katarzyna Pietruska-Paluba
We prove the existence of the integrated density of states for subordinate Brownian motions in presence of the Poissonian random potentials on the Sierpiński gasket.
Poincaré Inequality and Hajlasz-Sobolev spaces on nested fractals
Katarzyna Pietruska-Pałuba, Andrzej Stos
Given a nondegenerate harmonic structure, we prove a Poincaré-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajlasz-Sobole…
Orlicz-space Hardy and Landau-Kolmogorov inequalities for Gaussian measures
Krzysztof Oleszkiewicz, Katarzyna Pietruska-Paluba
We prove Orlicz-space versions of Hardy and Landau-Kolmogorov inequalities for Gaussian measures on the n-dimensional Euclidean space.
On a variant of Gagliardo-Nirenberg inequality deduced from Hardy
Agnieszka Kalamajska, Katarzyna Pietruska-Paluba
We obtain new variants of weighted Gagliardo-Nirenberg interpolation inequalities in Orlicz spaces, as a consequence of weighted Hardy-type inequalities. The weights we consider ne…
On a variant of Hardy inequality between weighted Orlicz spaces
Agnieszka Kalamajska, Katarzyna Pietruska-Paluba
Let M be an N-function satisfying the - condition, let $ω, \vp$ be two other functions, . We study Hardy-type inequalities \[ \int_{\rp} M(ω(x)|u(x)|) {\rm exp}(-\vp (…
Probabilistic characterisation of Besov-Lipschitz spaces on metric measure spaces
Katarzyna Pietruska-Pałuba
We give a probabilistic characterisation of the Besov-Lipschitz spaces on domains which support a Markovian kernel with appropriate exponential bounds. This extends…
Some function spaces related to the Brownian motion on simple nested fractals
Katarzyna Pietruska-Paluba
In this paper we identify the domain of the Dirichlet form associated with the Brownian motion on simple nested fractals with an integral Lipschitz space. This result generalizes s…