In this paper, using a generalized Jacobi-Dunkl translation operator, we prove a generalization of Titchmarsh’s theorem for functions in the k-JacobiDunkl-Lipschitz class defined by the finite differences of order k ∈ N∗ and Sobolev spaces associated with the Jacobi-Dunkl operator.

We study persistence properties of solutions to some canonical dispersive models, namely the semi-linear Schrödinger equation, the k-generalized Korteweg-de Vries equation and the Benjamin-Ono equation, in weighted Sobolev spaces Hs(Rn) ∩ L2(|x|ldx), s, l > 0.

Morrey Spaces were first introduced by C.B. in 1938. space can be considered as a generalization of the Lebesgue spaces. spaces then generalized become spaces, weighted and One studies on is boundedness certain operators fractional integral. The integrals classical had been known. extensions operator was bounded purpose this study to investigate weight used Muckenhoupt class. results obtained s...

In this paper, we establish generalized sampling theorems, stability theorems and new inequalities in the setting of shift-invariant subspaces Lebesgue Wiener amalgam spaces with mixed-norms. A convergence theorem general iteration algorithms for some Lp→(Rd) are also given.

We show that a big Hankel operator on the standard Hardy space of the polydisk D, n > 1, cannot be compact unless it is the zero operator. We also show that this result can be generalized to certain Hankel operators defined on Hardy-Sobolev spaces of the polydisk.

Abstract: In this paper, by using the Galerkin method and the generalized Brouwer’s theorem, some problems of the higher eigenvalues are studied for a class of singular quasiliner elliptic equations in the weighted Sobolev spaces. The existence of weak solutions is obtained for this problem.

The purpose of this article is to give a simple characterization of chaos for certain weighted composition C0-semigroups on Lebesgue spaces and Sobolev spaces over open intervals. Recall that a C0-semigroup T on a separable Banach space X is called chaotic if T is hypercyclic, i.e. there is x ∈ X such that {T (t)x; t ≥ 0} is dense in X , and if the set of periodic points, i.e. {x ∈ X ; ∃t > 0 :...

In this paper we introduce a generalization of the classical L2(R)-based Sobolev spaces with the help of a vector differential operator P which consists of finitely or countably many differential operators Pn which themselves are linear combinations of distributional derivatives. We find that certain proper full-space Green functions G with respect to L = P∗TP are positive definite functions. H...

and Applied Analysis 3 2. Finite Element Method We adopt the standard notation for Sobolev spaces W Ω with 1 ≤ p ≤ ∞ consisting of functions that have generalized derivatives of order s in the space L Ω . The norm of W Ω is defined by