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

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

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