In this paper, some necessary and sufficient conditions for sup{kx : ‖x‖ = 1} < ∞ in Musielak-Orlicz function spaces as well as in Musielak-Orlicz sequence spaces are given.

In this paper, we introduce generalized difference sequence spaces via ideal convergence, lacunary of χ sequence spaces over p−metric spaces defined by Musielak function, and examine the Musielak-Orlicz function which satisfies uniform ∆2 condition, and we also discuss some topological properties of the resulting spaces of χ with respect to ideal structures which is solid and monotone. Hence, g...

We introduce a new class of Hardy spaces H(R), called Hardy spaces of Musielak-Orlicz type, which generalize the Hardy-Orlicz spaces of Janson and the weighted Hardy spaces of Garćıa-Cuerva, Strömberg, and Torchinsky. Here, φ : R × [0,∞) → [0,∞) is a function such that φ(x, ·) is an Orlicz function and φ(·, t) is a MuckenhouptA∞ weight. A function f belongs to H(R) if and only if its maximal fu...

*Correspondence: [email protected] College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, P.R. China Abstract Anisotropy is a common attribute of Nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathematics, can be expressed by a fairly general discret...

In the present paper, we introduce some sequence spaces using ideal convergence and Musielak-Orlicz function ℳ = (M(k)). We also examine some topological properties of the resulting sequence spaces.

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.

Abstract. In this paper, we give necessary and sufficient conditions for a point in a Musielak-Orlicz sequence space equipped with the Orlicz norm to be an H-point. We give necessary and sufficient conditions for a Musielak-Orlicz sequence space equipped with the Orlicz norm to have the Kadec-Klee property, the uniform Kadec-Klee property and to be nearly uniformly convex. We show that a Musiel...

In the present paper we introduced some multiplier sequence spaces defined by a Musielak-Orlicz function M = (Mk) in n-normed spaces and examine some topological properties and some inclusion relation between the resulting sequence spaces.

and Applied Analysis 3 Proposition 1.2. Function σ t is μ-measurable. Proof. Pick a dense set {ri}i 1 in 0,∞ and set Bk { t ∈ T : M ( t, 1 2 rk ) 1 2 M t, rk } , qk t rkχBk t k ∈ N . 1.7 It is easy to see that for all k ∈ N, σ t ≥ qk t μ-a.e on T . Hence, supk≥1qk t ≤ σ t . For μ-a.e t ∈ T , arbitrarily choose ε ∈ 0, σ t . Then, there exists rk ∈ σ t − ε, σ t such that M t, 1/2 rk 1/2 M t, rk ,...

In this article, we introduce a new class of ideal convergent sequence spaces using an infinite matrix, Musielak-Orlicz function and a new generalized difference matrix in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We also give some relations related to these sequence spaces.