where the supremum is taken over all cubes Q ⊂ R containing the point x. In [5], L. Diening proved the following remarkable result: if p− > 1, p+ < ∞ and M is bounded on Lp(·), then M is bounded on L (·), where p′(x) = p(x) p(x)−1 . Despite its apparent simplicity, the proof in [5] is rather long and involved. In this paper we extend Diening’s theorem to weighted variable Lebesgue spaces L p(·)...

the purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of sturm-liouville problem with equation of the form w??=(?2f(x)?r(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in c2(a,b which has a single zero (so called turning point) at point 0x=x and r(x) is a continuously differentiable function. ...

Let X be a real Banach space. A multivalued operator T from K into 2 is said to be pseudo-contractive if for every x, y in K, u ∈ T (x), v ∈ T (y) and all r > 0, ‖x−y‖ ≤ ‖(1+r)(x−y)−r(u−v)‖. Denote by G(z, w) the set {u ∈ K : ‖u−w‖ ≤ ‖u−z‖}. Suppose every bounded closed and convex subset of X has the fixed point property with respect to nonexpansive selfmappings. Now if T is a Lipschitzian and ...

Let G be a locally compact non-compact group. We show that under a very mild assumption on the weight function w, the weighted group algebra L1(G, w) is strongly Arens irregular in the sense of [Dal–Lam–Lau 01]. To this end, we first derive a general factorization theorem for bounded families in the L∞ ( G, w ) ∗ -module L∞ ( G, w ) .

Kurzfassung: Objekt-relationale Datenbanksysteme (ORDBS) bieten heute zahlreiche Erweiterungsmöglichkeiten. Über Erweiterungsschnittstellen ist es möglich, Teile der sonst in der separaten Anwendung vorhandenen Funktionalität in das ORDBS zu integrieren. Mittlerweile lassen sich sogar komplette Anwendungsdienste in Form eines Servers in das ORDBS integrieren, um so eine datennahe Verarbeitung z...

The cutwidth of a graph G is defined to be the smallest integer k such that the vertices of G can be arranged in a vertex ordering [v1, . . . , vn] in a way that, for every i = 1, . . . , n− 1, there are at most k edges with one endpoint in {v1, . . . , vi} and the other in {vi+1, . . . , vn}. We examine the problem of computing in polynomial time the cutwidth of a partial w-tree with bounded d...

The main result of this paper is a generalization of a theorem of R. S. Phillips [6] on the nonexistence of projections of l°° onto c0. If S is a locally compact Hausdorff space then let C(S) denote the space of bounded continuous real (or complex) valued functions on 5; also, let Co(S) be those functions in C(S) which vanish at infinity. If N is the space of positive integers with the discrete...

where ε > 0 is very small and Σ ⊂ R is Lipschitz, open and bounded. A point of Σε is denoted by (x, x3) with x ∈ Σ and x3 ∈]− ε 2 , ε 2 [. Let W : M 3×3 → [0,+∞] be the stored-energy function supposed to be continuous and coercive, i.e., W (F ) ≥ C|F | for all F ∈ M and some C > 0. In order to take into account the important physical properties that the interpenetration of matter does not occur...