Continuity of the Outer Factorization and Mapping Properties with Applications

This paper investigates the smoothness behavior of the Poosson- and the conjugate Poisson integral on the closure of the unit disk. It gives sufficient and necessary conditions on the majorants of the data such that these integrals as well as the Hilbert- and Cauchy transform have always the same modulus of continuity as the data, provided that the data have no zeros on the unit circle. The results are applied to study the smoothness properties of the spectral factorization and Wiener filter.