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The finite Hilbert transform in weighted spaces

Published online by Cambridge University Press:  14 November 2011

Kari Astala ,
Lassi Päivärinta  and
Eero Saksman
Kari Astala
Affiliation:
Department of Mathematics, University of Helsinki, PL 4 (Hallituskatu 15), 00014 University of Helsinki, Finland
Lassi Päivärinta
Affiliation:
Department of Mathematical Sciences, University of Oulu, Linnanmaa, 90570 Oulu, Finland
Eero Saksman
Affiliation:
Department of Mathematics, University of Helsinki, PL 4 (Hallituskatu 15), 00014 University of Helsinki, Finland
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Abstract

The mapping properties of the finite Hilbert-transform (respectively the Hilbert transform on the half axis) are studied. Invertibility, surjectivity, injectivity and bounded ness from below of the transform are characterised in general weighted spaces. The results are applied to the restriction of the operator with logarithmic kernel.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 6 , 1996 , pp. 1157 - 1167
Copyright
Copyright © Royal Society of Edinburgh 1996

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