In this paper we introduce strongly $left[  V_{2},lambda_{2},M,pright]-$summable double vsequence spaces via Orlicz function and examine someproperties of the resulting these spaces. Also we give natural relationshipbetween these spaces and $S_{lambda_{2}}-$statistical convergence.

In this work two versions of weak Orlicz spaces that appear in the literature, MA and MA, are analyzed. One of those include the weak Lebesgue spaces for 1 :5 p < 00, while the other version gives these spaces only for p > 1, resulting the stronger space L1 in the extrem case p = 1. Necessary and sufficient condit.ions about t.he growth function A in order that. both spaces coincide arc given. ...

We deal with Orlicz-Sobolev embeddings in open subsets of R. A necessary and sufficient condition is established for the existence of an optimal, i.e. largest possible, Orlicz-Sobolev space continuously embedded into a given Orlicz space. Moreover, the optimal Orlicz-Sobolev space is exhibited whenever it exists. Parallel questions are addressed for Orlicz-Sobolev embeddings into Orlicz spaces ...

Recently, Gardner, Hug and Weil developed an Orlicz-Brunn1 Minkowski theory. Following this, in the paper we further consider the 2 Orlicz-Brunn-Minkowski theory. The fundamental notions of mixed quer3 massintegrals, mixed p-quermassintegrals and inequalities are extended to 4 an Orlicz setting. Inequalities of Orlicz Minkowski and Brunn-Minkowski 5 type for Orlicz mixed quermassintegrals are o...

We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in [Formula: see text]. We also make an effort to prove that every symmetric normalized block Orlicz-Garling sequen...

Let fi, i = 1, . . . , n, be copies of a random variable f and N be an Orlicz function. We show that for every x ∈ R 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 provide appl...

We give necessary and sufficient conditions for the boundedness of generalized fractional integral maximal operators on Orlicz–Morrey weak spaces. To do this, we prove weak–weak type modular inequality Hardy–Littlewood operator with respect to Young function. spaces contain L p $L^p$ ( 1 ≤ ∞ $1\le p\le \infty$ ), Orlicz spaces, Morrey as special cases. Hence, get these function corollaries.

The aim of this paper is to introduce and study a new concept ofstrong double $(A)_ {Delta}$-convergent sequence offuzzy numbers with respect to an Orlicz function and also someproperties of the resulting sequence spaces of fuzzy   numbers areexamined. In addition, we define the double$(A,Delta)$-statistical convergence of fuzzy  numbers andestablish some connections between the spaces of stron...

Composition operators C− between Orlicz spaces L.;6;1⁄4/ generated by measurable and nonsingular transformations − from  into itself are considered. We characterize boundedness and compactness of the composition operator between Orlicz spaces in terms of properties of the mapping − , the function ' and the measure space .;6;1⁄4/. These results generalize earlier results known for L p-spaces....