In this paper, we introduce some new sequence space using Orlicz function and study some properties of this space.

We consider an Orlicz space based cohomology for metric (measured) spaces with bounded geometry. We prove the quasi-isometry invariance for a general Young function. In the hyperbolic case, we prove that the degree one cohomology can be identified with an Orlicz-Besov function space on the boundary at infinity. We give some applications to the large scale geometry of homogeneous spaces with neg...

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...

Let fi , i = 1, . . . , n, be copies of a random variable f and let N be an Orlicz function. We show that for every x ∈ Rn the expectation E‖(xifi )i=1‖N is maximal (up to an absolute constant) if fi , i = 1, . . . , n, are independent. In that case we show that the expectation E‖(xifi)i=1‖N is equivalent to ‖x‖M , for some Orlicz function M depending on N and on distribution of f only. We prov...

In the article we generalize Marcinkiewicz sampling theorem in context of Orlicz spaces. We establish conditions under which holds terms restricted submultiplicativity and supermultiplicativity an N-function $$\varphi $$ , boundedness Hilbert transform Matuszewska-Orlicz indices. addition give a new criterion for on space.

The objective of this paper is to present a comprehensive study of dual representations of risk measures and convex functionals defined on an Orlicz space L or an Orlicz heart H. The first part of our study is devoted to the Orlicz pair (L, L). In this setting, we present a thorough analysis of the relationship between order closedness of a convex set C in L and the closedness of C with respect...

We obtain the equivalence of the properties (β) and (NUC) in Orlicz function spaces. This answers a question raised by Y. Cui, R. Pluciennik and T. Wang.

In this article we discuss lattice convexity and concavity of Calderón-Lozanovskii space Eφ , generated by a quasi-Banach space E and an increasing Orlicz function φ. We give estimations of convexity and concavity indices of Eφ in terms of Matuszewska-Orlicz indices of φ as well as convexity and concavity indices of E. In the case when Eφ is a rearrangement invariant space we also provide some ...

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. They have been studied by many authors, including Masty lo, Maligranda, and Kamińska. In this paper, we consider the problem of comparing the Orlicz–Lorentz norms, and establish necessary and sufficient conditions for them to be equivalent. As a corollary, we give necessary and sufficient conditions for a...