K. Astala et al., THE FINITE HILBERT TRANSFORM IN WEIGHTED SPACES, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 126, 1996, pp. 1157-1167
The mapping properties of the finite Hilbert-transform (respectively t
he Hilbert transform on the half axis) are studied. Invertibility, sur
jectivity, injectivity and boundedness from below of the transform are
characterised in general weighted spaces. The results are applied to
the restriction of the operator with logarithmic kernel.