THE FINITE HILBERT TRANSFORM IN WEIGHTED SPACES

Authors
ASTALA K PAIVARINTA L SAKSMAN E
Citation
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
Citations number
11
Categorie Soggetti
Mathematics, General",Mathematics,Mathematics
Journal title
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics → ACNP
ISSN journal
03082105
Volume
126
Year of publication
1996
Part
6
Pages
1157 - 1167
Database
ISI
SICI code
0308-2105(1996)126:<1157:TFHTIW>2.0.ZU;2-S
Abstract
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.