Induktive Limites gewichteter Räume stetiger und holomorpher Funktionen.
For large classes of indices, we characterize the weights u, v for which the Hardy operator is bounded from into . For more general operators of Hardy type, norm inequalities are proved which extend to weighted amalgams known estimates in weighted -spaces. Amalgams of the form , 1 < p,q < ∞ , q ≠ p, , are also considered and sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator and local maximal operator in these spaces are obtained.
Probabilistic normed linear spaces (briefly PNL spaces) were first studied by A. N. Serstnev in [1]. His definition was motivated by the definition of probabilistic metric spaces (PM spaces) which were introduced by K. Menger and subsequebtly developed by A. Wald, B. Schweizer, A. Sklar and others.In a previuos paper [2] we studied the relationship between two important classes of PM spaces, namely E-spaces and pseudo-metrically generated PM spaces. We showed that a PM space is pseudo-metrically...