The finite Hilbert transform acting on $L^\infty$

Guillermo P. Curbera; Susumu Okada; Werner J. Ricker

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arXiv · 2602.04844

The finite Hilbert transform acting on $L^\infty$

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

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Abstract

The action of the finite Hilbert transform defined on $L^\infty(-1,1)$ and taking its values in the Zygmund space $L_{\textnormal{exp}}(-1,1)$ is studied in detail. This is a reciprocal situation to the investigation recently undertaken in [11] of the finite Hilbert transform defined on the Zygumd space $L\textnormal{log} L(-1,1)$ and taking its values in $L^1(-1,1)$. The fact that both $L^\infty(-1,1)$ and $L_{\textnormal{exp}}(-1,1)$ fail to be separable generates new features not present in[11].

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BibTeX RIS

Guillermo P. Curbera, Susumu Okada, Werner J. Ricker. 2026-02-04. The finite Hilbert transform acting on $L^\infty$. https://arxiv.org/abs/2602.04844

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