Orlicz Function Spaces Research Articles

Best proximity points in modular function spaces

We generalize the notion of best proximity points in the context of modular function spaces. We have found sufficient conditions for the existence and uniqueness of best proximity points for cyclic maps in modular function spaces. We present an application of the main result for cyclic integral operators in Orlicz function spaces, endowed with an Orlicz function modular.

A Study of Behavior of the Sequence of Norm of Primitives of Functions in Orlicz Spaces Depending on Their Spectrum

In this paper we characterize behavior of the sequence of norm of primitives of functions in Orlicz spaces by its spectrum (the support of its Fourier transform).

Degree of Approximation for Nonlinear Multivariate Sampling Kantorovich Operators on Some Functions Spaces

In this article, the problem of the order of approximation for the nonlinear multivariate sampling Kantorovich operators is investigated. The case of uniformly continuous and bounded functions belonging to Lipschitz classes is considered, as well as the case of functions in Orlicz spaces. In the latter setting, suitable Zygmung-type classes are introduced by using the modular functionals of the spaces. The results obtained show that the order of approximation depends on both the kernels of our operators and the engaged functions. Several examples of kernels are considered in special instances of Orlicz spaces, typically used in approximation theory and for applications to signal and image processing.

The Daugavet property in the Musielak–Orlicz spaces

We show that among all Musielak–Orlicz function spaces on a σ-finite non-atomic complete measure space equipped with either the Luxemburg norm or the Orlicz norm the only spaces with the Daugavet property are L1, L∞, L1⊕1L∞ and L1⊕∞L∞. In particular, we obtain complete characterizations of the Daugavet property in the weighted interpolation spaces, the variable exponent Lebesgue spaces (Nakano spaces) and the Orlicz spaces.

Completely Continuous Composition Operators on Orlicz Spaces

Let ϕ : X → X be a non-singular transformation, ψ be an Orlicz function and (X, Σ ,μ )ac ompleteσ-finite measure space. In this paper, by using Radon-Nikodym derivative dμ◦ϕ �1 dμ , the compact composition operator Cϕf = f ◦ ϕ on Orlicz space L ψ (μ) is characterized. The sufficient and necessary condition for the bounded composition operator to be completely continuous is obtained. Keywords: Orlicz function; Orlicz space; composition operator; complete continuousness MR(2010) Subject Classification: 47B38; 47B33; 47B37 / CLC number: O177.2 Document code: A Article ID: 1000-0917(2015)01-0111-06

Approximative Compactness and Radon-Nikodym Property inw∗Nearly Dentable Banach Spaces and Applications

Authors definew∗nearly dentable Banach space. Authors study Radon-Nikodym property, approximative compactness and continuity metric projector operator inw∗nearly dentable space. Moreover, authors obtain some examples ofw∗nearly dentable space in Orlicz function spaces. Finally, by the method of geometry of Banach spaces, authors give important applications ofw∗nearly dentability in generalized inverse theory of Banach space.

Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces

In this paper, the problem of the order of approximation for the multivariate sampling Kantorovich operators is studied. The cases of uniform approximation for uniformly continuous and bounded functions/signals belonging to Lipschitz classes and the case of the modular approximation for functions in Orlicz spaces are considered. In the latter context, Lipschitz classes of Zygmund-type which take into account of the modular functional involved are introduced. Applications to $L^p(\R^n)$, interpolation and exponential spaces can be deduced from the general theory formulated in the setting of Orlicz spaces. The special cases of multivariate sampling Kantorovich operators based on kernels of the product type and constructed by means of Fej\'er's and B-spline kernels have been studied in details.

A strict topology on Orlicz spaces

Let ϕ be a Young function, Ω be a locally compact space, and μ be a positive Radon measure on Ω. We consider a strict topology βϕ (in the sense of Sentilles-Taylor) on the Orlicz function space Mϕ(Ω) and investigate various properties of this locally convex topology. We also study the Orlicz space Mϕ(G) of a locally compact group G with a left Haar measure under the strict topology βϕ and certain other natural locally convex topologies. Finally we present some results on various continuity properties of convolution operators on Mϕ(G) under the βϕ topology and other natural ones

Order of approximation for sampling Kantorovich operators

In this paper, we study the problem of the rate of approximation for the family of sampling Kantorovich operators in the uniform norm, for uniformly continuous and bounded functions belonging to Lipschitz classes (Zygmund-type classes), and for functions in Orlicz spaces. The general setting of Orlicz spaces allows us to directly deduce the results concerning the order of approximation in $L^p$-spaces, $1 \le p \lt \infty$, very useful in applications to Signal Processing, in Zygmund spaces and in exponential spaces. Particular cases of the sampling Kantorovich series based on Fej\'er's kernel and B-spline kernels are studied in detail.

Uniform nonsquareness and locally uniform nonsquareness in Orlicz–Bochner function spaces and applications

In this paper, criteria for uniform nonsquareness and locally uniform nonsquareness of Orlicz–Bochner function spaces equipped with the Orlicz norm are given. Although, criteria for uniform nonsquareness and locally uniform nonsquareness in Orlicz function spaces were known, we can easily deduce them from our main results. Moreover, we give a sufficient condition for an Orlicz–Bochner function space to have the fixed point property.

Perturbation classes of semi-Fredholm operators in Banach lattices

We prove some results giving positive answers to the perturbation classes problem for semi-Fredholm operators acting on Banach lattices satisfying certain conditions, and we show that these results can be applied to some Lorentz and Orlicz function spaces.

Smoothness and approximative compactness in Orlicz function spaces

Some criteria for approximative compactness of every weakly$^{*}$ closed convex set of Orlicz function spaces equipped with the Luxemburg norm are given. Although, criteria for approximative compactness of Orlicz function spaces equipped with the Luxemburg norm were known, we can easily deduce them from our main results.

Capacitary Orlicz spaces, Calderón products and interpolation

These notes are devoted to the analysis on a capacity space, with capacities as substitutes of measures of the Orlicz function spaces. The goal is to study some aspects of the classical theory of Orlicz spaces for these spaces including the classical theo

On Banach Space Valued Orlicz Function Space l (X, U, ||.||, ξ ) and its Generalized Form l (X, U, ||.||, ξ, λ, p)

On Banach Space Valued Orlicz Function Space l (X, U, ||.||, ξ ) and its Generalized Form l (X, U, ||.||, ξ, λ, p)

Order of approximation for nonlinear sampling Kantorovich operators in Orlicz spaces

In this paper, we study the rate of approximation for the nonlinear sampling Kantorovich operators. We consider the case of uniformly continuous and bounded functions belonging to Lipschitz classes of the Zygmund-type, as well as the case of functions in Orlicz spaces. We estimate the aliasing errors with respect to the uniform norm and to the modular functional of the Orlicz spaces, respectively. The general setting of Orlicz spaces allows to deduce directly the results concerning the rate of convergence in \(L^p\)-spaces, \(1 \miu p\) < \(\infty\), very useful in the applications to Signal Processing. Others examples of Orlicz spaces as interpolation spaces and exponential spaces are discussed and the particular cases of the nonlinear sampling Kantorovich series constructed using Fej\'er and B-spline kernels are also considered.

Complex interpolation of Orlicz spaces with respect to a vector measure

We apply the Calderón interpolation methods to Orlicz and weakly Orlicz function spaces with respect to a Banach-space-valued measure defined on a σ-algebra. The results we obtain generalize those in the case of Banach lattices of p-integrable and weakly p-integrable functions with respect to such a vector measure.

Nonlinear centralizers with values in [formula omitted

It is shown that every centralizer from any “metric function space” X to L0 is continuous at the origin of X. As a consequence, every short exact sequence of L∞-modules 0→L0→Z→X→0 splits if X is a “minimal” function space, and in particular if X=L0. There are pairs of Orlicz function spaces U,V such that Hom(U,V)=0, but Ext(U,V)≠0.

Ball-Covering Property in Uniformly Non- Banach Spaces and Application

This paper shows the following. (1) is a uniformly non- space if and only if there exist two constants such that, for every 3-dimensional subspace of , there exists a ball-covering of with or which is -off the origin and . (2) If a separable space has the Radon-Nikodym property, then has the ball-covering property. Using this general result, we find sufficient conditions in order that an Orlicz function space has the ball-covering property.

A generalization of the Riesz–Fischer theorem and linear summability methods

We extend the classical Riesz–Fischer theorem to biorthogonal systems of functions in Orlicz spaces: from a given double series (not necessarily convergent but satisfying a growth condition) we construct a function (in a given Orlicz space) by a linear summation method, and recover the original double series via the coefficients of the expansion of this function with respect to the biorthogonal system. We give sufficient conditions for the regularity of some linear summation methods for double series. We are inspired by a result of Fomin who extended the Riesz–Fischer theorem to Lp spaces.

Uniform Gateaux differentiability and weak uniform rotundity in Musielak–Orlicz function spaces of Bochner type equipped with the Luxemburg norm

Criteria for weak uniform rotundity and reflexivity of Musielak–Orlicz function spaces of Bochner type equipped with the Luxemburg norm are given. Although, criteria for uniform Gateaux differentiability and weak uniform rotundity of Musielak–Orlicz function spaces of real functions equipped with the Luxemburg norm were known, they can be also easily deduced from our main results.