The Pełczyński and Dunford–Pettis properties of the space of uniform convergent Fourier series with respect to orthogonal polynomials

Abstract

The Banach space U (µ) of uniformly convergent Fourier series with respect to an orthonormal polynomial sequence with orthogonalization measure µ supported on a compact set S ⊂ R is studied. For certain measures µ, involving Bernstein-Szegö polynomials and certain Jacobi polynomials, it is proven that U (µ) has the Pełczyński property, and also that U (µ) and U (µ) have the Dunford-Pettis property.