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arXiv · 1908.09542

The optimal symmetric quasi-Banach range of the discrete Hilbert transform

K. S. Tulenov
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Abstract

We identify symmetric quasi-Banach range of the discrete Calder\'{o}n operator and Hilbert transform acting on a symmetric quasi-Banach sequence space. As an application we present an example of optimal range in the case when the domain of those operators is the weak-$\ell_{1}$ space of sequences.

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K. S. Tulenov. 2019-08-26. The optimal symmetric quasi-Banach range of the discrete Hilbert transform. https://doi.org/10.1007/s00013-019-01375-w

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