Superlinear equations, potential theory and weighted norm inequalities
In questo lavoro si studiano condizioni sufficienti sulla funzione peso , espresse in termini di integrabilità, per la validità della disuguaglianza dove denota una sfera in . Usando una tecnica di decomposizione di immersioni si dimostrano condizioni sufficienti in termini di appartenenza a spazi di Lebesgue, Lorentz-Orlicz e/o di tipo debole. Come applicazioni vengono fornite condizioni sufficienti per la proprietà forte di prolungamento unico per nelle dimensioni 2 e 3.
We study the superposition operator f on on the space ac 0 of sequences almost converging to zero. Conditions are derived for which f has a representation of the form f x = a+bx +g x, for all x ∈ ac 0 with a = f 0, b ∈ D(ac 0), g a superposition operator from ℓ∞ into I(ac 0), D(ac 0) = {z: zx ∈ ac 0 for all x ∈ ac 0}, and I(ac 0) the maximal ideal in ac 0. If f is generated by a function f of a real variable, then f is linear. We consider the conditions for which a bounded function f generates f...
We characterize the set of all functions f of R to itself such that the associated superposition operator Tf: g → f º g maps the class BVp1(R) into itself. Here BVp1(R), 1 ≤ p < ∞, denotes the set of primitives of functions of bounded p-variation, endowed with a suitable norm. It turns out that such an operator is always bounded and sublinear. Also, consequences for the boundedness of superposition operators defined on Besov spaces Bp,qs are discussed.
Upper semi-Fredholm operators and tauberian operators in Banach spaces admit the following perturbative characterizations [6], [2]: An operator T: X --> Y is upper semi-Fredholm (tauberian) if and only if for every compact operator K: X --> Y the kernel N(T+K) is finite dimensional (reflexive). In [7] Tacon introduces an intermediate class between upper semi-Fredholm operators and tauberian operators, the supertauberian operators, and he studies this class using non-standard analysis....
Support functionals in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm are completely characterized. An explicit formula for regular support functionals is given. For obtaining a characterization of singular support functionals a generalized Banach limit is applied. Some necessary and sufficient conditions for smooothness of these spaces are given, too.