= Directional Hilbert transform
{title2=$H_vg(x)=\pi^{-1}\operatorname{pv}\int_{\mathbb R}g(x-sv)\,ds/s$}
For a unit vector $v$, the directional <Hilbert transform> integrates along lines parallel to $v$. Its <Fourier multiplier> is $-i\operatorname{sgn}(\xi\cdot v)$ under the usual transform convention. Applied to a rectangle whose long axis is $v$, it reduces to the one-dimensional logarithmic tail of an interval <indicator function>, separately on each transverse coordinate.
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