Weighted Orlicz Spaces Research Articles

On non-effective weights in Orlicz spaces

Given a weight w in Ω ⊂ ∝ N, |Ω| < ∞ and a Young function φ, we consider the weighted modular ∫ Ω ω(f(x))w(x)dx and the resulting weighted Orlicz space L ω(w). For a Young function Ω ∉ Δ 2(∞) we present a necessary and sufficient conditions in order that L ω(w) = L ω(X Ω) up to the equivalence of norms. We find a necessary and sufficient condition for ω in order that there exists an unbounded weight w such that the above equality of spaces holds. By way of applications we simplify criteria from [5] for continuity of the composition operator from L ω into itself when ω Δ 2(∞) and obtain necessary and sufficient condition in order that the composition operator maps L ω. continuously onto L ω.

Approximation by trigonometric polynomials in weighted Orlicz spaces

Approximation by trigonometric polynomials in weighted Orlicz spaces

Gagliardo–Nirenberg inequalities in weighted Orlicz spaces

Gagliardo–Nirenberg inequalities in weighted Orlicz spaces

Weighted inequalities for Cesàro maximal operators in Orlicz spaces

Let 0 &lt; α ≤ 1 and let M+α be the Cesàro maximal operator of order α defined by In this work we characterize the pairs of measurable, positive and locally integrable functions (u, v) for which there exists a constant C &gt; 0 such that the inequality holds for all λ &gt; 0 and every f in the Orlicz space LΦ(v). We also characterize the measurable, positive and locally integrable functions w such that the integral inequality holds for every f ∈ LΦ(w). The discrete versions of this results allow us, by techniques of transference, to prove weighted inequalities for the Cesàro maximal ergodic operator associated with an invertible measurable transformation, T, which preserves the measure.Finally, we give sufficient conditions on w for the convergence of the sequence of Cesàro-α ergodic averages for all functions in the weighted Orlicz space LΦ(w).

The Schur and (weak) Dunford-Pettis properties in Banach lattices

AbstractWe study the Schur and (weak) Dunford-Pettis properties in Banach lattices. We show that l1, c0 and l∞ are the only Banach symmetric sequence spaces with the weak Dunford-Pettis property. We also characterize a large class of Banach lattices without the (weak) Dunford-Pettis property. In MusielakOrlicz sequence spaces we give some necessary and sufficient conditions for the Schur property, extending the Yamamuro result. We also present a number of results on the Schur property in weighted Orlicz sequence spaces, and, in particular, we find a complete characterization of this property for weights belonging to class ∧. We also present examples of weighted Orlicz spaces with the Schur property which are not L1-spaces. Finally, as an application of the results in sequence spaces, we provide a description of the weak Dunford-Pettis and the positive Schur properties in Orlicz spaces over an infinite non-atomic measure space.

Interpolation orbits in couples of [formula omitted] spaces

We consider linear operators T mapping a couple of weighted L p spaces { L p 0 ( U 0), L p 1 ( U 1)} into { L q 0 ( V 0), L q 1 ( V 1)} for any 1⩽ p 0, p 1, q 0, q 1⩽∞, and describe the interpolation orbit of any a∈ L p 0 ( U 0)+ L p 1 ( U 1) that is we describe a space of all { Ta}, where T runs over all linear bounded mappings from { L p 0 ( U 0), L p 1 ( U 1)} into { L q 0 ( V 0), L q 1 ( V 1)}. We show that interpolation orbit is obtained by the Lions–Peetre method of means with functional parameter as well as by the K-method with a weighted Orlicz space as a parameter. To cite this article: V.I. Ovchinnikov, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 881–884.

Interpolation methods of constants and means with quasi-power function parameters

The purpose of this paper is to describe the interpolation methods of constants and means with quasi-power function parameters in the sense of Brudnyi-Krugljak's K- and J-methods with the weighted Orlicz space parameters. As an application, the relationship of such methods with particular parameters and the complex methods for Banach spaces of Fourier type is sharpened.

An inequality on weighted Orlicz spaces for a vector-valued extension of the Hardy-Littlewood maximal operator on S^n and P^n(ℝ)

An inequality on weighted Orlicz spaces for a vector-valued extension of the Hardy-Littlewood maximal operator on S^n and P^n(ℝ)

Weak type inequalities for fractional maximal operator on weighted orlicz spaces

The fractional maximal operator on homogeneous space (X, d, μ) is de fined as Open image in new window . In this paper, the sufficient and necessary conditions for the Open image in new window to be of weak type and extra weak type will be given.

DECOMPOSITION FOR BERS-ORLICZ SPACES

In this paper some decomposition theorems for classical weighted Orlicz spaces and Bers-Orlicz spaces are established. As applications of these decomposition theorems some estimates about the growth of the Taylor coefficients of the functions in Bers-Orlicz spaces are given.

Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator

Necessary and sufficient conditions are given for the Hardy-Littlewood maximal operator to be bounded on a weighted Orlicz space when the complementary Young function satisfies $Δ_2$. Such a growth condition is shown to be necessary for any weighted integ

On Imbeddings between Weighted Orlicz Spaces

Necessary and sufficient conditions are given for weight functions \varrho and \sigma , which guarantee validity of the imbedding between the Orlicz spaces L_{Q,\varrho} \hookrightarrow L_{P, \sigma} . We make use of two methods: the first of them is a limit procedure leading to the imbedding of weighted Zygnwnd classes into weighted L_1 , the second method employs the concept of duality in weighted Orlicz spaces, index of a Young function and results in a general imbedding theorem.

Approximation and entropy numbers of embeddings in weighted Orlicz spaces

Approximation and entropy numbers of embeddings in weighted Orlicz spaces