Geodesic
Hilbert's transformation and $A$-integral
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 4, pp. 1239-1243.

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We prove that if $g$ is a bounded function, $g\in L^p(\mathbb R)$, $p\ge1$, its Hilbert's transformation $\tilde g$ is also a bounded function, and $f(x)\in L(\mathbb R)$, then $\tilde fg$ is an $A$-integrable function on $\mathbb R$ and $$ (A)\!\int\limits_{\mathbb R}\tilde fg\,dx =-(L)\!\int\limits_{\mathbb R}f\tilde g\,dx. $$ 
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Anter Ali Alsayad. Hilbert's transformation and $A$-integral. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 4, pp. 1239-1243. http://geodesic.mathdoc.fr/item/FPM_2002_8_4_a20/

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