Appell orthogonal polynomials on the unit circle
If the Poisson integral of the unit disc is replaced by its square root, it is known that normalized Poisson integrals of and weak boundary functions converge along approach regions wider than the ordinary nontangential cones, as proved by Rönning and the author, respectively. In this paper we characterize the approach regions for boundary functions in two general classes of Orlicz spaces. The first of these classes contains spaces having the property , . The second contains spaces that...
We investigate the approximation properties of the partial sums of the Fourier series and prove some direct and inverse theorems for approximation by polynomials in weighted Orlicz spaces. In particular we obtain a constructive characterization of the generalized Lipschitz classes in these spaces.
Soient et deux groupes abéliens localement compacts de dual et . Soit un homomorphisme continu d’image dense de dans . Soit ; on prouve un théorème d’approximation des multiplicateurs de et on utilise ce résultat pour démontrer le suivant : soit une fonction continue ; est un multiplicateur de si, et seulement si, est un multiplicateur de .
The direct and inverse problems of approximation theory in the subspace of weighted generalized grand Lebesgue spaces of 2π-periodic functions with the weights satisfying Muckenhoupt's condition are investigated. Appropriate direct and inverse theorems are proved. As a corollary some results on constructive characterization problems in generalized Lipschitz classes are presented.