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- Bartłomiej Dyda
- 2004

We investigate the following integral inequality: ∫ D |u(x)|p dist(x,Dc)α dx ≤ c ∫

- Bartłomiej Dyda
- 2006

We prove comparability of certain homogeneous anisotropic integral forms. As a consequence we obtain a Hardy type inequality generalising that for the fractional Laplacian. We give an application to… (More)

We significantly expand the number of functions whose image under the fractional Laplace operator can be computed explicitly. In particular, we show that the fractional Laplace operator maps Meijer… (More)

The aim of this note is to show that Poincare inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincare inequalities are considered, too. The proof is short… (More)

A steering installation for motor vehicles, particularly trucks, which essentially includes a steering spindle, a steering column, a vertically adjustable steering wheel, and vehicle operating and… (More)

We study a certain improved fractional Sobolev–Poincaré inequality on domains, which can be considered as a fractional counterpart of the classical Sobolev–Poincaré inequality. We prove the… (More)

- Bartłomiej Dyda
- 2010

We prove norm inequalities between Lorentz and Besov–Lipschitz spaces of fractional smoothness. 1. Main results. In what follows we let (F, ρ) be a metric space with a positive σ-finite Borel measure… (More)

We characterize conditional Hardy spaces of the Laplacian and the fractional Laplacian by using Hardy-Stein type identities.

Let X be a metric space equipped with a doubling measure. We consider weights w(x) = dist(x,E)−α, where E is a closed set in X and α∈ℝ$\alpha \in \mathbb {R}$. We establish sharp conditions, based on… (More)

- Bartłomiej Dyda, J. Tugaut
- 2017

This article deals with a mean-field model. We consider a large number of particles interacting through their empirical law. We know that there is a unique invariant probability for this diffusion.… (More)