Mariusz Żyluk

activity

20192023

collaborators

5 papers

math.FA2023

Density of compactly supported smooth functions $C_{C}^{\infty} (R^{d})$ in Musielak-Orlicz-Sobolev spaces $W^{1, Φ} (Ω)$

Anna Kamiśka, Mariusz Żyluk

We investigate here the density of the set of the restrictions from $C_{C}^{\infty} (R^{d})$ to $C_{C}^{\infty} (Ω)$ in the Musielak-Orlicz-Sobolev space $W^{1, Φ} (Ω)$ . It is a continu…

math.FA2023

Density of smooth functions in Musielak-Orlicz-Sobolev spaces $W^{k, Φ} (Ω)$

Anna Kaminśka, Mariusz Żyluk

We consider here Musielak-Orlicz Sobolev (MOS) spaces $W^{k, Φ} (Ω)$ , where $Ω$ is an open subset of $R^{d}$ , $k \in N$ and $Φ$ is a Musielak-Orlicz function. The main…

math.FA2022

Density of smooth functions in Musielak-Orlicz spaces

Anna Kamińska, Mariusz Żyluk

We provide necessary and sufficient conditions for the space of smooth functions with compact supports $C_{C}^{\infty} (Ω)$ to be dense in Musielak-Orlicz spaces $L^{Φ} (Ω)$ where $Ω$ is a…

math.FA2021

Uniform convexity, reflexivity, supereflexivity and $B$ convexity of generalized Sobolev spaces $W^{1, Φ}$

Anna Kamińska, Mariusz Żyluk

We investigate Sobolev spaces $W^{1, Φ}$ associated to Musielak-Orlicz spaces $L^{Φ}$ . We first present conditions for the boundedness of the Voltera operator in $L^{Φ}$ . Employing this…

math.FA2019

Local geometric properties in quasi-normed Orlicz spaces

Anna Kamińska, Mariusz Żyluk

Several local geometric properties of Orlicz space $L_{ϕ}$ are presented for an increasing Orlicz function $ϕ$ which is not necessarily convex, and thus $L_{ϕ}$ does not need to be a B…

Density of compactly supported smooth functions CC∞​(Rd) in Musielak-Orlicz-Sobolev spaces W1,Φ(Ω)

Density of smooth functions in Musielak-Orlicz-Sobolev spaces Wk,Φ(Ω)

Density of smooth functions in Musielak-Orlicz spaces

Uniform convexity, reflexivity, supereflexivity and B convexity of generalized Sobolev spaces W1,Φ

Local geometric properties in quasi-normed Orlicz spaces

Density of compactly supported smooth functions $C_{C}^{\infty} (R^{d})$ in Musielak-Orlicz-Sobolev spaces $W^{1, Φ} (Ω)$

Density of smooth functions in Musielak-Orlicz-Sobolev spaces $W^{k, Φ} (Ω)$

Uniform convexity, reflexivity, supereflexivity and $B$ convexity of generalized Sobolev spaces $W^{1, Φ}$