FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

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

Anter Ali Alsayad

Abstract

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

$\$\$\; (A)\backslash int\_\{\backslash mathbb\; R\}\; \backslash tilde\; f\; g\; dx\; =$-(L)\int_{\mathbb R} f \tilde g dx.
$$
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Last modified: April 10, 2003