In this paper, we investigate several two-parameter weak Orlicz–Hardy martingale spaces generated by the $p$-convex and $q$-concave functions, establish their atomic decomposition theorems. Using decomposition, obtain a sufficient condition for boundedness of sublinear operator defined on spaces. Furthermore, dual are considered.

An alternative interpretation of a family of weighted Carleson measures is used to characterize p-Carleson measures for a class of Hardy-Orlicz spaces admitting a nice weak factorization. As an application, we provide with a characterization of symbols of bounded weighted composition operators and Cesàro-type integral operators from these Hardy-Orlicz spaces to some classical holomorphic functi...

for all z1; . . . ; zn 2 C and all n 1 . The constant p 2 is shown to be the best possible. The method of proof relies upon a combinatorial argument, Taylor expansion, and the central limit theorem. The result is additionally strengthened by showing that the underlying functions are Schur-concave. The proof of this fact uses a result on multinomial distribution of Rinott, and Schur’s propositio...

We prove an extension of McDiarmid’s inequality for metric spaces with unbounded diameter. To this end, we introduce the notion of the subgaussian diameter, which is a distribution-dependent refinement of the metric diameter. Our technique provides an alternative approach to that of Kutin and Niyogi’s method of weakly difference-bounded functions, and yields nontrivial, dimension-free results i...

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 extend the M -condition from [10] and introduce the Φ -condition at zero. Next we discuss nonsquare constant in Orlicz spaces generated by an N -function Φ(u) which satisfy Φ -condition. We obtain exact value of nonsquare constant in this class of Orlicz spaces equipped with the Luxemburg norm.

In this paper we introduce a new concept for lacunary strong P-convergent with respect to an Orlicz function and examine some properties of the resulting sequence space of fuzzy numbers. We also show that if a sequence is lacunary strong Pconvergence with respect to an Orlicz function then it is , ( ) r s S F θ -convergent.

For Lp spaces on Td, Rd and Sd−1 sharp versions of the classical Marchaud inequality are known. These results are extended here to Orlicz spaces (on Td, Rd and Sd−1) for which M(u1/q) is convex for some q, 1 < q ≤ 2, where M(u) is the Orlicz function. Sharp converse inequalities for such spaces are deduced.

We show that Korn’s inequality in Orlicz spaces holds if and only if the Orlicz function satisfies the ∆2and the ∇2-condition. This result applies to several types of Korn’s inequality. In particular we show that Korn’s inequality is false in L, in L logL, in Exp and in L∞. MSC (2000): 74 B, 74 G, 76 D, 49 J.

Let χ denotes the space of all double gai sequences. Let Λ denotes the space of all double analytic sequences. This paper is devoted to a study of the general properties of Nörlund double Orlicz space of gai sequence space η ( χM ) and χM . and Nörlund double Orlicz space of analytic sequence space η ( ΛM ) and ΛM .