Si K es un compacto no vacío en Rr, damos una condición suficiente para que la inyección canónica de ε{M},b(K) en ε{M},d(K) sea nuclear. Consideramos el caso mixto y obtenemos la existencia de un operador de extensión nuclear de ε{M1}(F)A en ε{M2}(Rr)D donde F es un subconjunto cerrado propio de Rr y A y D son discos de Banach adecuados. Finalmente aplicamos este último resultado al caso Borel, es decir cuando F = {0}.
Necessary and sufficient condition on the weights will be derived under which a -th order Hardy inequality holds on classes of functions satisfying more than “boundary” conditions.
Let be a real number and let be an even integer. We determine the largest value such that the inequality holds for all real numbers which are pairwise distinct and satisfy . Our theorem completes results of Ozeki, Mitrinović-Kalajdžić, and Russell, who found the optimal value in the case and odd, and in the case and even.
We prove that if f: → is Darboux and has a point of prime period different from , i = 0,1,..., then the entropy of f is positive. On the other hand, for every set A ⊂ ℕ with 1 ∈ A there is an almost continuous (in the sense of Stallings) function f: → with positive entropy for which the set Per(f) of prime periods of all periodic points is equal to A.