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Non-extendability of the finite Hilbert transform


Curbera, GP and Okada, S and Ricker, WJ, Non-extendability of the finite Hilbert transform, Monatshefte fur Mathematik, 195, (4) pp. 649-657. ISSN 0026-9255 (2021) [Refereed Article]

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Copyright (2021) TheAuthor(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.

DOI: doi:10.1007/s00605-021-01572-2


The finite Hilbert transform T:X -> X acts continuously on every rearrangement invariant space X on (-1,1) having non-trivial Boyd indices. It is proved that T cannot be further extended, whilst still taking its values in X, to any larger domain space. That is, T:X -> X is already optimally defined.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Pure mathematics not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Okada, S (Dr Susumu Okada)
ID Code:152494
Year Published:2021
Deposited By:Mathematics
Deposited On:2022-08-19
Last Modified:2022-09-14
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