Sia $E$ uno spazio $DF$ riflessivo e sia $K$ un compatto di $E$. Si dimostra che lo spazio dei germi olomorfi su $K$, con la topologia naturale, è un limite induttivo regolare e quasi completo purché lo spazio dei germi olomorfi all'origine sia un limite induttivo regolare.

We prove that a K-quasiconformal mapping f:ℝ² → ℝ² which maps the unit disk onto itself preserves the space EXP() of exponentially integrable functions over , in the sense that u ∈ EXP() if and only if $u\circ f^{-1}\in EXP\left(\right)$. Moreover, if f is assumed to be conformal outside the unit disk and principal, we provide the estimate $1/(1+KlogK)\le \left(\right||u\circ f^{-1}{\left|\right|}_{EXP\left(\right)}{)/(\left|\right|u\left|\right|}_{EXP\left(\right)})\le 1+KlogK$ for every u ∈ EXP(). Similarly, we consider the distance from $L^{\infty }$ in EXP and we prove that if f: Ω → Ω’ is a K-quasiconformal mapping and G ⊂ ⊂ Ω, then $1/K\le \left(dis{t}_{EXP\left(f\right(G\left)\right)}(u\circ f^{-1},L^{\infty }\left(f\left(G\right)\right))\right)/\left(dis{t}_{EXP\left(f\right(G\left)\right)}(u,L^{\infty }\left(G\right))\right)\le K$ for every u ∈ EXP(). We also prove that...

We examine how Poincaré change under quasiconformal maps between appropriate metric spaces having the same Hausdorff dimension. We also show that for many metric spaces the Sobolev functions can be identified with functions satisfying Poincaré, and this allows us to extend to the metric space setting the fact that quasiconformal maps from ${ℝ}^Q$ onto ${ℝ}^Q$ preserve the Sobolev space $L^{1,Q}\left({ℝ}^Q\right)$.

We consider quasiconformal mappings in the upper half space ${ℝ}_{+}^{n+1}$ of ${ℝ}^{n+1}$, $n\ge 2$, whose almost everywhere defined trace in ${ℝ}^n$ has distributional differential in $L^n\left({ℝ}^n\right)$. We give both geometric and analytic characterizations for this possibility, resembling the situation in the classical Hardy space $H^1$. More generally, we consider certain positive functions defined on ${ℝ}_{+}^{n+1}$, called conformal densities. These densities mimic the averaged derivatives of quasiconformal mappings, and we prove analogous trace theorems for them....

A quasi-linear map from a continuous function space C(X) is one which is linear on each singly generated subalgebra. We show that the collection of quasi-linear functionals has a Banach space pre-dual with a natural order. We then investigate quasi-linear maps between two continuous function spaces, classifying them in terms of generalized image transformations.

A class of locally convex vector spaces with a special Schauder decomposition is considered. It is proved that the elements of this class, which includes some spaces naturally appearing in infinite dimensional holomorphy, are quasinormable though in general they are neither metrizable nor Schwartz spaces.

Pour tout compact complètement régulier $T$, on désigne par $M_{\beta }\left(T\right)$ l’espace des mesures de Radon sur le compactifié de Stone-Cech $\beta T$ de $T$ et par $M_{\sigma }\left(T\right)$ son sous-espace formé des mesures $\sigma$-régulières au sens de Varadarajan. On décrit alors sur ces deux espaces des topologies ${\mathbf{T}}_p$, $1\le p\le +\infty$, qui possèdent des propriétés curieuses parmi lesquelles il convient de citer la suivante : pour $1\<p\le +\infty$ et pour tout $T$ non pseudocompact, l’espace $\left(M_{\sigma }\right(T),{\mathbf{T}}_p)$ est non quasi-complet mais ses précompacts sont relativement compacts. Ce résultat permet...