Criteria in order that an Orlicz space equipped with the Orlicz norm contains a linearly isometric copy (or an order linearly isometric copy) of l1 (or l∞) are given.

The classical Minkowski problem lead to the Lp Minkowski problem and now to the Orlicz-Minkowski problem. Existence is demonstrated for the even Orlicz-Minkowski problem. A byproduct is a new approach to the solution of the classical Minkowski problem.

In Musilak-Orlicz type spaces ${\mathcal S}_{\bf M}$, direct and inverse approximation theorems are obtained in terms of the best approximations functions generalized moduli smoothness. The question exact constants Jackson-type inequalities is studied.

Abstract We study properties of $\mathcal {A}$ A -harmonic and -superharmonic functions involving an operator having generalized Orlicz growth. Our framework embraces reflexive spaces, as well natural variants variable exponent double-phase spaces. In particular, Harnack’s Principle Minimum are provided for f...

In this paper we prove compact embedding of a subspace the fractional Orlicz-Sobolev space $W^{s, G}\left(\mathbb{R}^{N}\right)$ consisting radial functions, our target spaces are Orlicz type. Also, Lions and Lieb type results for $W^{s,G}\left(\mathbb{R}^{N}\right)$ that works together in particular way to get sequence whose weak limit is nontrivial. As an application, study existence solution...

The aim of this paper is to characterize one-complemented subspaces of finite codimension in the Musielak–Orlicz sequence space l . We generalize the well-known fact (Ann. Mat. Pura Appl. 152 (1988) 53; Period. Math. Hungar. 22 (1991) 161; Classical Banach Spaces I, Springer, Berlin, 1977) that a subspace of finite codimension in lp, 1 p<∞, is one-complemented if and only if it can be expressed...

Let φ : ℝ(n) × [0, ∞)→[0, ∞) be a Musielak-Orlicz function and A an expansive dilation. In this paper, the authors introduce the anisotropic Hardy space of Musielak-Orlicz type, H(A)(φ)(ℝ(n)), via the grand maximal function. The authors then obtain some real-variable characterizations of H(A)(φ)(ℝ(n)) in terms of the radial, the nontangential, and the tangential maximal functions, which general...

In this paper we introduced the Orlicz space of χπ. We establish some inclusion relations, topological results and we characterize the duals of the Orlicz of χπ sequence spaces. 2000 Mathematics Subject Classification: 40A05,40C05,40D05.