Let φφ be an Orlicz function that has a complementary function φφ∗ and let llφφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev’s Sum Inequality in llφφ⨂� FFXX, the Fremlin projective tensor product of llφφ with a Banach lattice X, and in llφφ⨂� iiXX, the Wittstock injective tensor product of llφφ with a Banach lattice X.

We establish uniform estimates for order statistics: Given a sequence of independent identically distributed random variables ξ1, . . . , ξn with log-concave distribution and scalars x1, . . . , xn, for every k ≤ n we provide estimates for E kmin1≤i≤n |xiξi| and E k-max1≤i≤n |xiξi| in terms of the value k and the appropriate Orlicz norm ‖(1/x1, . . . , 1/xn)‖M , associated with the distribution...

Let χ denote the space of all double gai sequences. Let Λ denote the space of all double analytic sequences. This paper is to introduce a new class of sequence spaces namely the semi difference Orlicz space of Λ. It is shown that the intersection of all semi difference Orlicz space of Λ is I ⊂ η and Λ ⊂ I.

Abstract In this short paper, I recall the history of dealing with lack compactness a sequence in case an unbounded domain and prove vanishing Lions-type result for Lebesgue-measurable functions. This lemma generalizes some results class Orlicz–Sobolev spaces. What matters here is behavior integral, not space.