Weighted Orlicz Spaces Research Articles

APPROXIMATION OF FUNCTIONS BY THE MATRIX MEANS IN WEIGHTED ORLICZ SPACES

Abstract. In this work, the approximation properties of the matrix submethods in weighted Orlicz spaces L T M , are investigated. We obtain some results related to trigonometric approximation using matrix submethods of partial sums of Fourier series of functions in weighted Orlicz spaces.The degree of trigonometric approximations by the matrix methods to the functions have been investigated in weighted Orlicz spaces. The error of estimations in this work is obtained in more general terms.

Weighted Orlicz regularity for fully nonlinear elliptic equations with oblique derivative at the boundary via asymptotic operators

We prove weighted Orlicz-Sobolev regularity for fully nonlinear elliptic equations with oblique boundary condition under asymptotic conditions of the following problem{F(D2u,Du,u,x)=f(x)inΩβ⋅Du+γu=gon∂Ω, where Ω is a bounded domain in Rn (n≥2), under suitable assumptions on the source term f, data β,γ and g. Our approach guarantees such estimates under conditions where the governing operator F does not require a convex (or concave) structure. We also deal with weighted Orlicz-type estimates for the obstacle problem with oblique derivative condition on the boundary. As a final application, the developed methods provide weighted Orlicz-BMO regularity for the Hessian, provided that the source lies in that space and in weighted Orlicz space associated.

Integrability for Hardy operators of double phase

We establish Hardy–Sobolev and Hardy–Trudinger inequalities in weighted Orlicz spaces on \mathbb{R}^n . As an application, we prove Hardy–Sobolev and Hardy–Trudinger inequalities in the framework of general double phase functionals given by \varphi_p(x,t) = \varphi_1(t^p) + \varphi_2((b(x)t)^p), \quad x\in \mathbb{R}^n,\, t \ge 0, where p>1 , \varphi_1, \varphi_2 are positive convex functions on (0,\infty) and b is a non-negative function on [0,\infty) which is Hölder continuous of order \theta \in (0,1] .

Convergence Results for Nonlinear Sampling Kantorovich Operators in Modular Spaces

In the present paper, convergence in modular spaces is investigated for a class of nonlinear discrete operators, namely the nonlinear multivariate sampling Kantorovich operators. The convergence results in the Musielak-Orlicz spaces, in the weighted Orlicz spaces, and in the Orlicz spaces follow as particular cases. Even more, spaces of functions equipped by modulars without an integral representation are presented and discussed.

Gradient estimates of general nonlinear singular elliptic equations with measure data

We develop a global Calderón-Zygmund estimate for the gradients of renormalized solutions to the general nonlinear singular elliptic equations −divA(x,u,Du)=μ on a Reifenberg flat domain with the homogeneous Dirichlet boundary condition, while μ is a finite signed Radon measure. The associated nonlinearity behaves as the elliptic p-Laplacian with respect to Du for the singular case p∈(1,2−1/n], whose discontinuity in the x-variable is measured in terms of small BMO, and the Lipschitz continuity is required with respect to the u-variable. We prove it in two folds: the perturbation technique and the weighted Vitali type covering are first employed to establish the weighted good-λ type inequality, then such inequality is used to prove the desired global gradient estimates in weighted Lorentz spaces and Lorentz-Morrey spaces. As a direct consequence, finally we obtain a global gradient regularity in weighted Orlicz spaces.

Local potential operator and uniform resolvent estimate for generalized Schrödinger operator in Orlicz spaces

AbstractThe local potential operator with integral kernel restricted in a ball of radius less than some fixed number has appeared frequently in the spectral estimates of the Schrödinger operator. In this paper, we establish a good‐λ inequality for this operator and characterize its uniform boundedness on the weighted Orlicz space in both strong and weak senses. The uniformity in r of this boundedness enables us to recover the classical boundedness of “global” potential operator, by letting . As an application, we establish uniform estimate for the resolvent of some generalized Schrödinger operator on the Orlicz space. An explicit representation in its operator norm on the dependence of is also given.

Disjoint topological transitivity for cosine operator functions on weighted Orlicz spaces

In this note, we give sufficient conditions for sequences of operators to be disjoint topologically transitive on the weighted Orlicz spaces of locally compact groups. This condition also ensures the disjoint blow-up/collapse property holds. In our case, these sequences of operators can be regarded as cosine operator functions. Disjoint topological mixing for such cosine operator functions is investigated as well.

Parabolic nonsingular integral operator and its commutators on weighted Orlicz space

Parabolic nonsingular integral operator and its commutators on weighted Orlicz space

A NEW TYPE OF WEIGHTED ORLICZ SPACES

In this paper, by some group action, we introduce a new type of weighted Orlicz spaces $L^\Phi_{w,v}(\Omega)$, where $w$ and $v$ are weights on $\Omega$ and $\Phi$ is a Young function. We study conditions under which $L^\Phi_{w,v}(G)$ is a convolution Banach algebra, where $G$ is a locally compact group.

Jackson type inequalities for differentiable functions in weighted Orlicz spaces

In the present work some Jackson Stechkin type direct theorems of trigonometric approximation are proved in Orlicz spaces with weights satisfying some Muckenhoupt A p A_p condition. To obtain a refined version of the Jackson type inequality, an extrapolation theorem, Marcinkiewicz multiplier theorem, and Littlewood–Paley type results are proved. As a consequence, refined inverse Marchaud type inequalities are obtained. By means of a realization result, an equivalence is found between the fractional order weighted modulus of smoothness and Peetre’s classical weighted K K -functional.

On variational inequalities on exterior domains with multivalued convection terms

In this paper, we study variational inequalities of the form 〈−ΔNu,v−u〉+〈F(u),v−u〉≥0,∀v∈Ku∈K,where ΔNu=div|∇u|N−2∇u is the N-Laplacian, K is a closed convex set in the Beppo–Levi space X=D01,N(Ω), where Ω is the exterior of the closed unit ball B(0,1)¯ in RN (N≥2).We are interested here in the case where F is given by a multivalued function f=f(x,u,∇u) that depends also on the gradient ∇u of the unknown function. We consider a functional analytic framework of the above problem, including conditions on the lower order term f such that the problem can be appropriately formulated in X and a related weighted Orlicz space, and the involved mappings have certain useful monotonicity-continuity properties.Existence of solutions in coercive and noncoercive cases are studied. In the noncoercive case, we follow a sub-supersolution approach and prove the existence of solutions of the above inequality under a multivalued local growth condition of Bernstein–Nagumo type.

-invariant weighted Orlicz spaces

In this paper, we prove that σ-compactness of a locally compact group G is a necessary condition for the weighted Orlicz space to be a convolution algebra, and for a class of Orlicz spaces we give an equivalent condition. Also, we show that if is -invariant, then there exists a constant c > 0 such that Φ(ω(st)) ≤ c ω(s)ω Φ (t) for locally a.e. s, t ∈ G, where ω Φ is a locally integrable function satisfying an inclusion property.

Supercyclic dynamics of translations on weighted Orlicz spaces

Supercyclic dynamics of translations on weighted Orlicz spaces

Approximation by linear means of Fourier series and realization functionals in weighted Orlicz spaces

Approximation by linear means of Fourier series and realization functionals in weighted Orlicz spaces

Universal family of translations on weighted Orlicz spaces

Universal family of translations on weighted Orlicz spaces

Multipliers for the Weighted Orlicz Spaces of a Locally Compact Abelian Group

Multipliers for the Weighted Orlicz Spaces of a Locally Compact Abelian Group

Konveks olması gerekmeyen genelleştirilmiş Young fonksiyonu ile üretilen Ağırlıklı Orlicz Uzaylarında yaklaşım

The aim of this paper is to investigate the order of approximation by some linear summation methods of trigonometric Fourier series in weighted Orlicz spaces which have generating Young functions not necessary to be convex. Obtained estimations base on the fractional modulus of smoothness and the best approximation. Furthermore, a convolution type operator is defined and its estimation by the best approximation is obtained.

The Modular Inequalities for Hardy-type Operators on Monotone Functions in Orlicz Space

This paper is devoted to the study of modular inequality for general Hardy–Copson type operator restricted on the cone of monotone functions from weighted Orlicz space with general weight.

Approximation by Vilenkin Polynomials in Weighted Orlicz Spaces

Direct and inverse theorems are proved for approximation by bounded Vilenkin systems in weighted Orlicz spaces. The equivalence between the K-functional constructed with help of generalized derivative and three types of realizations functionals is established. We also obtain a simultaneous approximation result.

Uniform estimates with data from generalized Lebesgue spaces in periodic structures

We study various types of uniform Calderón–Zygmund estimates for weak solutions to elliptic equations in periodic homogenization. A global regularity is obtained with respect to the nonhomogeneous term from weighted Lebesgue spaces, Orlicz spaces, and weighted Orlicz spaces, which are generalized Lebesgue spaces, provided that the coefficients have small BMO seminorms and the domains are δ-Reifenberg domains.