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

View as HTML     View as gif image    View as LaTeX source

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
$$
(A)\!\int\limits_{\mathbb R} \tilde f g\, dx =
-(L)\!\int\limits_{\mathbb R} f \tilde g\, dx.
$$

All articles are published in Russian.

Main page Contents of the journal News Search

Location: http://mech.math.msu.su/~fpm/eng/k02/k024/k02421t.htm.
Last modified: April 10, 2003