in this paper we introduce some new double sequence spaces using the orlicz function andexamine some properties of the resulting sequence spaces.

The aim of this paper is investigating of Orlicz spaces with exponential N function and correspondence Orlicz norm: we introduce some new equivalent norms, obtain the tail characterization, study the product of functions in Orlicz spaces etc. We consider some applications: estimation of operators in Orlicz spaces and problem of martingales convergence and divergence.

We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in [Formula: see text]. We also make an effort to prove that every symmetric normalized block Orlicz-Garling sequen...

In this paper we extend the result of [6] on the characteristic of convexity of Orlicz spaces to the more general case of Musielak-Orlicz spaces over a non-atomic measure space. Namely, the characteristic of convexity of these spaces is computed whenever the Musielak-Orlicz functions are strictly convex.

Orlicz–Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. In this paper, we investigate their Boyd indices. Bounds on the Boyd indices in terms of the Matuszewska–Orlicz indices of the defining functions are given. Also, we give an example to show that the Boyd indices and Zippin indices of an Orlicz–Lorentz space need not be equal, answering a question of Malig...

Orlicz–Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. In this paper, we investigate their Boyd indices. Bounds on the Boyd indices in terms of the Matuszewska–Orlicz indices of the defining functions are given. Also, we give an example to show that the Boyd indices and Zippin indices of an Orlicz–Lorentz space need not be equal, answering a question of Malig...

We characterize those measures μ for which the Hardy-Orlicz (resp. weighted Bergman-Orlicz) space HΨ1 (resp. AΨ1 α ) of the unit ball of CN embeds boundedly or compactly into the Orlicz space LΨ2 ( BN ,μ ) (resp. LΨ2 (BN ,μ)), when the defining functions Ψ1 and Ψ2 are growth functions such that L1 ⊂ LΨ j for i, j ∈ {1,2}, and such that Ψ2/Ψ1 is non-decreasing. We apply our result to the charact...

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...

The problem of strict convexity of the Besicovitch-Orlicz space of almost periodic functions is considered here in connection with the Orlicz norm. We give necessary and sufficient conditions in terms of the function φ generating the space. 2000 Mathematics Subject Classification: 46B20, 42A75.

In this paper we introduce and study some new sequence spaces of fuzzy numbers defined by I-convergence using the sequences of Orlicz functions, infinite matrix. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces. Key WordsIdeal, I -convergent, infinite matrix, Orlicz function, fuzzy number.