In this paper, we are concerned with some qualitative properties of the new fractional Musielak–Sobolev spaces WsLΦx,y such that generalized Poincaré type inequality and continuous compact embedding results. Moreover, prove any function in WsLΦx,y(Ω) may be extended to a WsLΦx,y(RN), Ω⊂RN is bounded domain class C0,1. addition, establish result relates complemented subspace WsLΦx,yRN. As an app...

We prove a number of results concerning the embedding of a Banach lattice X into an r. i. space Y. For example we show that if Y is an r. i. space on [0, oo) which is/7-convex for some/? > 2 and has nontrivial concavity then any Banach lattice X which is r-convex for some r > 2 and embeds into Y must embed as a sublattice. Similar conclusions can be drawn under a variety of hypotheses on Y; if ...

Let $L$ be a finite-dimensional Lie algebra. We say a subalgebra $H$ of $L$ is permutably complemented in $L$ if there is a subalgebra $K$ of $L$ such that $L=H+K$ and $Hcap K=0$. Also, if every subalgebra of $L$ is permutably complemented in $L$, then $L$ is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in partic...

Consider a finite collection $\{T_1, \ldots, T_J\}$ of differential operators with constant coefficients on $\mathbb{T}^n$ ($n\geq 2$) and the space smooth functions generated by this collection, namely, $f$ such that $T_j f \in C(\mathbb{T}^n)$, $1\leq j\leq J$. We prove if there are at least two linearly independent among their senior parts (relative to some mixed pattern homogeneity), then d...

 In network code setting, a constant dimension code is a set of k-dimensional subspaces of F nq . If F_q n is a nondegenerated symlectic vector space with bilinear form f, an isotropic subspace U of F n q is a subspace that for all x, y ∈ U, f(x, y) = 0. We introduce isotropic subspace codes simply as a set of isotropic subspaces and show how the isotropic property use in decoding process, then...