In this paper, we study the existence of infinite dimensional closed linear subspaces of a rearrangement invariant space on [0, 1] every nonzero element of which does not belong to any included rearrangement invariant space of the same class such that the inclusion operator is disjointly strictly singular. We consider Lorentz, Marcinkiewicz and Orlicz spaces. The answer is affirmative for Marci...

Let (Ω,A, μ) be a σ-finite nonatomic measure space and let Λw,φ be the Orlicz-Lorentz space. We study the Gateaux differentiability of the functional Ψw,φ(f) = ∞ ∫ 0 φ(f∗)w. More precisely we give an exact characterization of those points in the Orlicz-Lorentz space Λw,φ where the Gateaux derivative exists. This paper extends known results already on Lorent spaces, Lw,q , 1 < q <∞. The case q =...

For Bn the unit ball of Cn, we consider Hardy-Orlicz spaces of holomorphic functions H, which are preduals of spaces of BMOA type with weight. We characterize the symbols of Hankel operators that extend into bounded operators from the Hardy-Orlicz H1 into H2 . We also consider the closely related question of integrability properties of the product of two functions, one in H1 and the other one i...

Let Γ 2 π denote the space of all double entire rate sequences. Let Λ 2 π denote the space of all double analytic rate sequences. This paper is devoted to a study of the general properties of Nörlund double Orlicz space η Γ 2 f π of entire rate sequences and Nörlund double Orlicz space η Λ 2 f π of analytic rate sequences.

We study certain twisted sums of Orlics spaces with non-trivial type which can be viewed as Fenchel-Orlicz spaces on R2. We then show that a large class of Fenchel-Orlicz spaces on R" can be renormed to have property (M). In particular this gives a new construction of the twisted Hilbert space 22 and shows it has property (M), after an appropriate renorming.

Recently Antilla, Ball and Perissinaki proved that the squares of coordinate functions in ln p are negatively correlated. This paper extends their results to balls in generalized Orlicz norms on Rn. From this, the concentration of the Euclidean norm and a form of the Central Limit Theorem for the generalized Orlicz balls is deduced. Also, a counterexample for the square negative correlation hyp...

Let f be a function in an Orlicz space L and μ(f,L) be the set of all the best Φ-approximants to f, given a σ−lattice L. Weak type inequalities are proved for the maximal operator f∗ = supn |fn|, where fn is any selection of functions in μ(f,Ln), and Ln is an increasing sequence of σ-lattices. Strong inequalities are proved in an abstract set up which can be used for an operator as f∗.

The concept of strong almost convergence was introduced by Maddox in 1978 [Math. Proc. Camb. Philos. Soc., 83 (1978), 61-64] which has various applications. In this paper we introduce some new sequence spaces which arise from the notions of strong almost convergence and an Orlicz function in a seminormed space. A new concept of uniform statistical convergence in a seminormed space has also been...

Existence of global weak solutions to a spatially inhomogeneous kinetic model for coalescing particles is proved, each particle being identified by its mass, momentum and position. The large time convergence to zero is also shown. The cornestone of our analysis is that, for any nonnegative and convex function, the associated Orlicz norm is a Liapunov functional. Existence and asymptotic behavio...

Abstract – The aim of this paper is to introduce and study a new concept of strong double Δ ) A ( σ convergence sequences with respect to an Orlicz function, and some properties of the resulting sequence spaces were also examined. In addition, we define the Δ ) A ( σ -statistical convergence and establish some connections between the spaces of strong double Δ ) A ( σ -convergence sequences and ...