We give equivalent conditions for tensor product of Orlicz sequence spaces, then we obtain a necessary and sufficient condition for a class of matrix operators acting on Orlicz sequence spaces to be continuous and compact.

This work deals with the Orlicz space and Hardy-Orlicz classes generated by this space, which consist of analytic functions inside outside unit disk. The homogeneous Riemann boundary value problems piecewise continuous coefficients are considered in these classes. New characteristic is defined depends on whether power function belongs to or not. Relationship between Boyd indices established. co...

In this paper we prove a long-standing conjecture in the theory of twoweight norm inequalities. To state the conjecture and our result we recall a few facts about Orlicz spaces; see [3, Chapter 5] for complete details. Given a Young function A, the complementary function Ā is the Young function that satisfies t ≤ A−1(t)Ā−1(t) ≤ 2t, t > 0. We will say that a Young function Ā satisfies the B2 con...

Using recent characterizations of the compactness of composition operators on HardyOrlicz and Bergman-Orlicz spaces on the ball ([2, 3]), we first show that a composition operator which is compact on every Hardy-Orlicz (or Bergman-Orlicz) space has to be compact on H∞. Then, although it is well-known that a map whose range is contained in some nice Korányi approach region induces a compact comp...

In this paper, we introduce some new sequence spaces in n-normed defined by Museliak-Orlicz function. Also investigate topological properties and inclusion relations between these Spaces

Negative association for a family of random variables (Xi) means that for any coordinate–wise increasing functions f, g we have Ef(Xi1 , . . . , Xik )g(Xj1 , . . . , Xjl ) ≤ Ef(Xi1 , . . . , Xik )Eg(Xj1 , . . . , Xjl ) for any disjoint sets of indices (im), (jn). It is a way to indicate the negative correlation in a family of random variables. It was first introduced in 1980s in statistics, and...

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...