In this paper, as a main result for Morrey spaces, we prove that the set Mpq (Rn)n S q

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Let $1≤q≤α≤∞$. The sets $\{(L^q,l^p )^α (\mathbb R^d ); α≤p≤∞\}$ and $\{F(q,p,α) (\mathbb R^d),; α≤p≤∞ \}$ are two nondecreasing families of Banach spaces such that for both the Lebsegue space $L^α(\mathbb R^d)$ is the minimal element and the Morrey space $M_q^α(\mathbb R^d)$ is the maximal element. It is also known that for $1

Purpose: The purpose of this paper is to study the multilinear commutator in weighted Morrey space.Methods: We divide the multilinear commutator into four parts and apply with the methods of weighted Lebesgue space and Perez and Trujillo-Gonzalez.Results: Let b®= (b1, …, bm), bj ∈ BMO (Rn), 1£j£ m; we show that T[1]b is bounded on weighted Morrey spaces Lp,κ (w), 1<p<¥, 0<k<1, w∈Ap. When p=1, it is shown that T®b is weak type bounded on weighted Morrey space.Conclusions: We extend the results of the commutator in weighted Morrey space. In particular, for m=1, this result is also new in the classical commutator.

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In this work systems of sines $\sin \left(n+\beta \right)t,\, \, n=1,2, \ldots,$ and cosines $\cos \left(n-\beta \right)t,\, \, n=0,1,2, \ldots,$ are considered, where $\beta \in R-$is a real parameter. The subspace $M^{p,\alpha } \left(0,\pi \right)$ of the Morrey space $L^{p,\alpha } \left(0,\pi \right)$ in which continuous functions are dense is considered. Criterion   for the completeness, minimality and basicity of these systems with respect to the parameter $\beta $  in the subspace  $M^{p,\alpha } \left(0,\pi \right)$, $1

It is henceforth a commonplace; the science-fiction would be a refractory genre by nature against the definitive assimilation to the literary mainstream. We can say that the usual thematic of the genre, to which is added the irresistible propensity to prospect the future in all its forms, immunizes the SF against the “academic confinement” to the benefit of other forms of confinement. Indeed, the SF belongs to the great family of the paraliterature where the more or less listed subgenres are waiting to receive a likely definition. Popular genre which relies on a remarkable poetic, the SF is an open place to the imagination, to the verbal and the figurative creativity. It owns itself its subgenres, among other things, the space opera which was, in a way, the original matrix of the speculative fiction and of its contemporary imitators. The Sternberg’s work did not have a special vocation to feed the already rich world of the science-fiction. It constitutes however a new step liable to bring a touch of self-reflexivity, we will notice that, to the history of this genre. French: “Le Navigateur” de Jacques Sternberg ou la phylogenese parodiee du space opera C’est dorenavant un lieu commun, la science-fiction serait un genre par nature refractaire a l’assimilation definitive au mainstream litteraire. Nous dirons que les thematiques habituelles du genre, auxquelles viennent se meler l’irresistible propension a prospecter l’avenir sous toutes ses formes, immunisent la SF contre “l’enfermement academique” au profit d’un enfermement d’un autre genre. En effet, celle-ci appartient, comme on le sait, a la grande famille de la paralitterature ou se cotoient les sous-genres plus ou moins repertories en attente de recevoir un semblant de definition. Genre populaire s’appuyant sur une poetique singuliere, la SF est un lieu ouvert a l’imagination, a la creativite verbale et figurative. Elle possede elle-meme ses sous-genres, entre autres, le space opera qui fut en quelque sorte la matrice originelle de la fiction speculative et de ses emules contemporaines. L’oeuvre sternbergienne n’eut guere pour vocation de nourrir le repertoire deja riche de la science-fiction. Elle constitue neanmoins une etape non repertoriee susceptible d’apporter, nous le constaterons, une touche d’auto-reflexivite a l’histoire du genre.Keywords: Jacques Sternberg, Nouvelle, Science-Fiction, Space Opera, Aventure, Fiction Speculative