Piotr Michał Bies

collaborators

4 papers

math.AP2024

Decay of solutions of non-homogenous hyperbolic equations

Piotr Michał Bies

We consider conditions for the decay in time of solutions of non-homogenous hyperbolic equations. It is proven that solutions of the equations go to $0$ in $L^{2}$ at infinity if and…

math.AP2024

Time-asymptotics of a heated string

Piotr Michał Bies, Tomasz Cieślak

In the present paper, we study a model of a thermoelastic string that is initially heated. We classify all the possible asymptotic states when time tends to infinity of such a mode…

math.FA2023

Maximal operator in Musielak--Orlicz--Sobolev spaces

Piotr Michał Bies, Michał Gaczkowski, Przemysław Górka

We study the Hardy-Littlewood maximal operator in the Musielak-Orlicz-Sobolev space $W^{1, φ} (R^{n})$ . Under some natural assumptions on $φ$ we show that the maximal function…

math.FA2023

Maximal operator in Hölder spaces

Piotr Michał Bies, Michał Gaczkowski, Przemysław Górka

We study the maximal operator on the variable exponent Hölder spaces in the setting of metric measure spaces. The boundedness is proven for metric measure spaces satisfying an annu…