Structure theory of function spaces
Study of some noncooperative linear elliptic systems
Using an approximation method, we show the existence of solutions for some noncooperative elliptic systems defined on an unbounded domain.
Su una classe di equazioni paraboliche singolari
Su una estensione del metodo d'interpolazione complesso
Subelliptic Poincaré inequalities: the case p < 1.
We obtain (weighted) Poincaré type inequalities for vector fields satisfying the Hörmander condition for p < 1 under some assumptions on the subelliptic gradient of the function. Such inequalities hold on Boman domains associated with the underlying Carnot- Carathéodory metric. In particular, they remain true for solutions to certain classes of subelliptic equations. Our results complement the earlier results in these directions for p ≥ 1.
Sulla interpolazione di certi spazi di Sobolev con peso
Sulla interpolazione multilineare : una precisazione
Sums of Plane Waves, and the Range of the Random Transform.
Superposition of functions in Sobolev spaces of fractional order. A survey
Superposition of imbeddings and Fefferman's inequality
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.
Superposition operators and functions of bounded p-variation.
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.
Superposition operators in the Lebesgue spaces and differentiability of quasiadditive set functions.
Sur la théorie du potentiel dans les domaines de John.
Using rather elementary and direct methods, we first recover and add on some results of Aikawa-Hirata-Lundh about the Martin boundary of a John domain. In particular we answer a question raised by these authors. Some applications are given and the case of more general second order elliptic operators is also investigated. In the last parts of the paper two potential theoretic results are shown in the framework of uniform domains or the framework of hyperbolic manifolds.
Sur la transformation de Fourier des fonctions à valeurs vectorielles
Sur le théorème de division de Weierstrass
We prove a Weierstrass division formula for Whitney jets ∂̅-flat on arbitrary compact subsets of the complex plane. We also give results for Carleman classes.
Sur les inégalités GKS
Sur les injections entre espaces de Sobolev et espaces d'Orlicz et application au comportement a l'infini pour des équations des ondes semi-linéaires
Sur l'inégalité de Sobolev logarithmique des opérateurs de Laguerre à petit paramètre
Sur l'utilisation des suites inconditionellement sommables dans la théorie des espaces d'interpolation
Sur un probleme d'existence de Lions pour une equation differentielle opérationnelle