Untersuchungen zur abgeschnittenen Hilbert-Transformation von BMO-Funktionen und VMO-Funktionen

摘要

The behaviour of the truncated Hilbert transform for functions of bounded mean oscillation (BMO) and functions of vanishing mean oscillation (VMO) is investigated in the paper. It is shown that for VMO functions the truncated Hilbert transform is convergent in the BMO-norm to the Hilbert transform. A new characterization of VMO function is also given in the paper.