Let ω denote the set of natural numbers. We prove: for every mod-finite ascending chain $T_{\alpha }:\alpha <\lambda$ of infinite subsets of ω, there exists $ℳ\subset {\left[\omega \right]}^{\omega }$, an infinite maximal almost disjoint family (MADF) of infinite subsets of the natural numbers, such that the Stone-Čech remainder βψ∖ψ of the associated ψ-space, ψ = ψ(ω,ℳ ), is homeomorphic to λ + 1 with the order topology. We also prove that for every λ < ⁺, where is the tower number, there exists a mod-finite ascending chain $T_{\alpha }:\alpha <\lambda$, hence a ψ-space with Stone-Čech remainder...

We revisit Orlicz's proof of the square summability of the norms of the terms of an unconditionally convergent series in L¹. The result is then used to motivate abstract generalizations and concrete improvements.

Let ϕ and ψ be functions defined on [0,∞) taking the value zero at zero and with non-negative continuous derivative. Under very mild extra assumptions we find necessary and sufficient conditions for the fractional maximal operator $M_{\Omega }^{\alpha }$, associated to an open bounded set Ω, to be bounded from the Orlicz space $L^{\psi }\left(\Omega \right)$ into $L^{\varphi }\left(\Omega \right)$, 0 ≤ α < n. For functions ϕ of finite upper type these results can be extended to the Hilbert transform f̃ on the one-dimensional torus and to the fractional integral operator $I_{\Omega }^{\alpha }$, 0...

We study the sequence $u_n$, which is solution of $-div\left(a(x,𝔻u_n)\right)+{\Phi }^{\text{'}\text{'}}\left(\right|u_n\left|\right)u_n=f_n+g_n$ in $\Omega$ an open bounded set of ${𝐑}^N$ and $u_n=0$ on $\partial \Omega$, when $f_n$ tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the $N$-function $\Phi$, and prove a non-existence result.

We study the sequence un, which is solution of $-\mathrm{div}\left(a(x,\nabla u_n)\right)+{\Phi }^{\text{'}\text{'}}\left(\right|u_n\left|\right)u_n=f_n+g_n$ in Ω an open bounded set of RN and un= 0 on ∂Ω, when fn tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the N-function Φ, and prove a non-existence result.

Necessary and sufficient conditions are given for Orlicz sequence spaces equipped with the Orlicz norm to be uniformly rotund in a weakly compact set of directions, using only conditions on the generating function of the space.

Let $M$ be a von Neumann algebra, let $\varphi$ be a weight on $M$ and let $\Phi$ be $N$-function satisfying the $({\delta }_2,{\Delta }_2)$-condition. In this paper we study Orlicz spaces, associated with $M$, $\varphi$ and $\Phi$.

Let M be the Hardy-Littlewood maximal operator defined by:Mf(x) = supx ∈ Q 1/|Q| ∫Q |f| dx, (f ∈ Lloc(Rn)),where the supreme is taken over all cubes Q containing x and |Q| is the Lebesgue measure of Q. In this paper we characterize the Orlicz spaces Lφ*, associated to N-functions φ, such that M is bounded in Lφ*. We prove that this boundedness is equivalent to the complementary N-function ψ of φ satisfying the Δ2-condition in [0,∞), that is, sups&gt;0 ψ(2s) / ψ(s) &lt; ∞.