Given a Young function $\Phi$, we study the existence of copies of $c_0$ and ${\ell }_{\infty }$ in ${\mathrm{c}abv}_{\Phi }(\mu ,X)$ and in ${\mathrm{c}absv}_{\Phi }(\mu ,X)$, the countably additive, $\mu$-continuous, and $X$-valued measure spaces of bounded $\Phi$-variation and bounded $\Phi$-semivariation, respectively.

In this paper we prove a regularity result for very weak solutions of equations of the type $-divA(x,u,Du)=B(x,u,Du)$, where $A$, $B$ grow in the gradient like $t^{p-1}$ and $B(x,u,Du)$ is not in divergence form. Namely we prove that a very weak solution $u\in W^{1,r}$ of our equation belongs to $W^{1,p}$. We also prove global higher integrability for a very weak solution for the Dirichlet problem $$\left\{\begin{array}{cc}-divA(x,u,Du)=B(x,u,Du)\hfill & \text{in}\Omega ,u-u_o\in W^{1,r}(\Omega ,{ℝ}^m).\hfill \end{array}\right.$$

We consider and study several weak formulations of the Hessian determinant, arising by formal integration by parts. Our main concern are their continuity properties. We also compare them with the Hessian measure.

This paper presents some properties of singular functionals on Orlicz spaces, from which criteria for weak convergence and weak compactness in such spaces are obtained.

Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator $\psi C_{\varphi }$ acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces. Under some assumptions on the weights we give a characterization for such an operator to be bounded in terms of the weights involved as well as the functions ψ and ϕ

Si studiano alcune proprietà di un certo limite induttivo di spazi non-archimedei di funzioni continue. In particolare, si esamina la completezza di questo limite induttivo e si indaga il problema di quando lo spazio coincide con il proprio inviluppo proiettivo.

The paper establishes integral representation formulas in arbitrarily wide Banach spaces $b_{\omega }^p\left({ℝ}^n\right)$ of functions harmonic in the whole ${ℝ}^n$.

For Orlicz spaces with Orlicz norm, a criterion of W*UR point is given, and previous results about UR points and WUR points are amended.

In Orlicz spaces theory some strengthened version of the Jensen inequality is often used to obtain nice geometrical properties of the Orlicz space generated by the Orlicz function satisfying this inequality. Continuous functions satisfying the classical Jensen inequality are just convex which means that such functions may be described geometrically in the following way: a segment joining every pair of points of the graph lies above the graph of such a function. In the current paper we try to obtain...

Nous établissons des résultats d’interpolation non-standards entre les espaces de Besov et les espaces $L^1$ et $BV$, avec des applications aux lemmes de régularité en moyenne et aux inégalités de type Gagliardo-Nirenberg. La preuve de ces résultats utilise les décompositions dans des bases d’ondelettes.