(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 4, PAGES 1239-1243

## Hilbert's transformation and $A$-integral

Abstract

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We prove that if $g$ is a bounded function, $g$Î Lp(R), $p$³ 1, its Hilbert's transformation $\tilde g$ is also a bounded function, and $f\left(x\right)$Î L(R), then $\tilde f g$ is an $A$-integrable function on R and

$\left(A\right)\int_\left\{\mathbb R\right\} \tilde f g dx =$-(L)\int_{\mathbb R} f \tilde g dx. 

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