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arXiv · 1911.08375

Non-extendability of the finite Hilbert transform

Guillermo P. Curbera·Susumu Okada·Werner J. Ricker
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Abstract

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

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Guillermo P. Curbera, Susumu Okada, Werner J. Ricker. 2019-11-19. Non-extendability of the finite Hilbert transform. https://arxiv.org/abs/1911.08375

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