FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2002, VOLUME 8, NUMBER 4, PAGES 1239-1243
Anter Ali Alsayad
Abstract
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We prove that if $g$
is a bounded function,
$g \in L^p(\mathbb R)$ ,
$p \ge 1$ ,
its Hilbert's transformation
$\tilde g$
is also a bounded function,
and $f(x) \in L(\mathbb R)$ ,
then $\tilde f g$
is an $A$ -integrable
function on $\mathbb R$ and
$$
(A)\!\int\limits_{\mathbb R} \tilde f g\, dx =
-(L)\!\int\limits_{\mathbb R} f \tilde g\, dx.
$$
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Last modified: April 10, 2003