Katarzyna Pietruska-Pałuba

On function spaces related to fractional diffusions on d-sets

We prove that all the Dirichlet forms associated with certain diffusions on a d-set are equivalent and that their common domain is an integral Lipschitz space. We also provide an analytic characterisation of the walk dimension dw of a d-set F and show that all fractional diffusions on F share dw as their walk dimension.

Logarithmic Version of Interpolation Inequalities for Derivatives

A version of interpolation inequalities for derivatives in logarithmic Orlicz spaces is obtained where the first gradient of is estimated in terms of and its second gradient. One of the Orlicz functions considered is supposed to be . The motivation, examples and applications are discussed.

The Wiener Sausage Asymptotics on Simple Nested Fractals

Abstract We investigate the long-time asymptotics of the Wiener sausage modelled on the trajectory of the Brownian motion on simple nested fractals, getting bounds similar to those in the Euclidean case. To get the upper bounds, we use the Sznitmans enlargement of obstacles technique, adapted to the fractal case.

On Ulam's redistribution of energy problem

We continue the work on Ulams redistribution of energy problem started by D. Blackwell and R. D. Mauldin (Lett. Math. Phys.10, 149–153 (1985)). We prove that for any initial distribution μ with the first moment finite, its images under iteration of Ulam transformation weakly converge. Some properties of the limit measure (especially its absolute continuity) are examined.

Integrated density of states for Poisson–Schrödinger perturbations of subordinate Brownian motions on the Sierpiński gasket

We prove the existence of the integrated density of states for subordinate Brownian motions in the presence of the Poissonian random potentials on the Sierpinski gasket.

Orlicz-space Hardy and Landau–Kolmogorov inequalities for Gaussian measures

Abstract We prove Orlicz-space versions of Hardy and Landau–Kolmogorov inequalities for Gaussian measures on ℝn.