Recently, both the bilinear decompositions [Formula: see text] and were established. In this paper, authors prove in some sense that former is sharp, while latter not. To end, first introduce local Orlicz-slice Hardy space which contains text], a variant of Orlicz space, introduced by Bonami Feuto as special case, obtain its dual establishing characterizations via atoms, finite various maximal ...

In this work two versions of weak Orlicz spaces that appear in the literature, MA and MA, are analyzed. One of those include the weak Lebesgue spaces for 1 :5 p < 00, while the other version gives these spaces only for p > 1, resulting the stronger space L1 in the extrem case p = 1. Necessary and sufficient condit.ions about t.he growth function A in order that. both spaces coincide arc given. ...

Quite recently, an Orlicz Minkowski problem has been posed and the existence part of this problem for even measures has been presented. In this paper, the existence part of the Orlicz Minkowski problem for polytopes is demonstrated. Furthermore, we obtain a solution of the Orlicz Minkowski problem for general (not necessarily even) measures.

We show the density of smooth Sobolev functions Wk,∞(Ω)∩C∞(Ω) in Orlicz-Sobolev spaces Lk,Ψ(Ω) for bounded simply connected planar domains Ω and doubling Young Ψ.

In this paper, we introduce two general double sequence spaces χM (p) and Λ 2 M (p) using Orlicz functions. We establish some inclusion relations, topological results and we characterize the duals of these double sequence spaces. Mathematics Subject Classification (2010): 40A05, 40C05, 40D05.

In this paper we introduce certain new sequence spaces of fuzzy numbers defined by Iconvergence using sequences of Orlicz functions and a difference operator of orderm. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces. © 2011 Elsevier Ltd. All rights reserved.

In this paper we introduce some double entire difference sequence spaces of fuzzy numbers defined by a sequence of Orlicz functions M = (Mk,l). We also make an effort to study some topological properties and some inclusion relations between these spaces.

In this article we define different type of statistically convergent, statistically null and statistically bounded double sequence spaces on a semi-normed space by Orlicz functions. We study their different properties like solidness, denseness, symmetricity, completeness etc. We obtain some inclusion relations.

Upper estimates for the order of Gâteaux smoothness of bump functions in Orlicz– Lorentz spaces d(w,M,Γ), Γ uncountable, are obtained. The best possible order of Gâteaux differentiability in the class of all equivalent norms in d(w,M,Γ) is found.

We use Simonenko quantitative indices of an N -function Φ to estimate two parameters qΦ and QΦ in Orlicz function spaces L [0,∞) with Orlicz norm, and get the following inequality: BΦ BΦ−1 ≤ qΦ ≤ QΦ ≤ AΦ Aφ−1 , where AΦ and BΦ are Simonenko indices. A similar inequality is obtained in L[0, 1] with Orlicz norm.