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...

Free interpolation in Hardy spaces is characterized by the well-known Carleson condition. The result extends to Hardy-Orlicz spaces contained in the scale of classical Hardy spaces H, p > 0. For the Smirnov and the Nevanlinna classes, interpolating sequences have been characterized in a recent paper in terms of the existence of harmonic majorants (quasi-bounded in the case of the Smirnov class)...

In this paper, we first define spaces of single difference sequences defined by a sequence of Orlicz functions without convexity and investigate their properties. Then we extend this idea to spaces of double sequences and present a new matrix theoretic approach construction of such double sequence spaces.  

Let [Formula: see text] satisfy that [Formula: see text], for any given [Formula: see text], is an Orlicz function and [Formula: see text] is a Muckenhoupt [Formula: see text] weight uniformly in [Formula: see text]. The Musielak-Orlicz Hardy space [Formula: see text] is defined to be the set of all tempered distributions such that their grand maximal functions belong to the Musielak-Orlicz spa...

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...

Recently Antilla, Ball and Perissinaki proved that the squares of coordinate functions in ln p are negatively correlated. This paper extends their results to balls in generalized Orlicz norms on Rn. From this, the concentration of the Euclidean norm and a form of the Central Limit Theorem for the generalized Orlicz balls is deduced. Also, a counterexample for the square negative correlation hyp...

We present some properties of real valued functions of bounded generalized variation of Riesz–Orlicz type including weight and characterize Lipschitzian superposition Nemytskii operators which map between spaces (in fact, Banach algebras) of these functions.

in this paper, we first define spaces of single difference sequences defined by a sequence of orlicz functions without convexity and investigate their properties. then we extend this idea to spaces of double sequences and present a new matrix theoretic approach construction of such double sequence spaces.

In this paper, we establish the equivalence of entropy and renormalized solutions second-order elliptic equations with nonlinearities defined by Musielak-Orlicz functions right-hand side from space L1(Ω). nonreflexive Musielak-Orlicz-Sobolev spaces, prove existence uniqueness both Dirichlet problem in domains a Lipschitz boundary.