The Pełczyński and Dunford–Pettis properties of the space of uniform convergent Fourier series with respect to orthogonal polynomials
Volume 164 / 2021
Colloquium Mathematicum 164 (2021), 1-9
MSC: Primary 46E15; Secondary 42C05, 42C10.
DOI: 10.4064/cm7890-3-2020
Published online: 6 August 2020
Abstract
The Banach space $U(\mu )$ of uniformly convergent Fourier series with respect to an orthonormal polynomial sequence with orthogonalization measure $\mu $ supported on a compact set $S\subset {\mathbb R}$ is studied. For certain measures $\mu $, involving Bernstein–Szegö polynomials and certain Jacobi polynomials, it is proven that $U(\mu )$ has the Pełczyński property, and also that $U(\mu )$ and $U(\mu )^\star $ have the Dunford–Pettis property.
