arXiv subjects
Publications and source records attributed to EL-Houcine Ouali.
In this article, we show some density properties of smooth and compactly supported functions in fractional Musielak-Sobolev spaces essentially extending the results of Fiscella, Servadei, and Valdinoci obtained in the fractional Sobolev setting. The proofs of these properties are mainly based on a basic technique of convolution, joined with a cutoff, with some care needed in order not to exceed the original support.
In this paper, we introduce a new fractional Musielak-Sobolev space $Ws,Φx,y(Ω)$ where $Ω$ is an open subset in RN and we show some density properties of smooth and compactly supported functions in this space.
Let $G$ be an Orlicz function and let $ α, β, s$ be positive real numbers. Under certain conditions on the Orlicz function $ G $, we establish some continuous embeddings results between the fractional order Orlicz-Sobolev spaces defined on metric-measure spaces $W_s^{α, G}(X, d, μ)$ and the fractional Hajłasz-Orlicz-Sobolev spaces $M^{β, G}(X,d,μ)$.