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 Mat. Sb. (N.S.), 1988, Volume 136(178), Number 3(7), Pages 341–360 (Mi msb1746)

On the integrability of a conjugate function in $L^p$ with the polynomial weight

R. I. Gurielashvili

Abstract: For any $p>1$ and any real $\alpha$, $-\infty<\alpha<\infty$, conditions on a function $f\in L_\alpha^p$ ($L_\alpha^p$ is the set of $2\pi$-periodic measurable functions $f$ such that $|f(x)|^p|x|^\alpha$ is integrable on $(-\pi,\pi]$) are found that are necessary and sufficient for its conjugate function $\widetilde f$ to be in $L_\alpha^p$.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1989, 64:2, 339–358

Bibliographic databases:

UDC: 517.51
MSC: Primary 42A50; Secondary 46E30

Citation: R. I. Gurielashvili, “On the integrability of a conjugate function in $L^p$ with the polynomial weight”, Mat. Sb. (N.S.), 136(178):3(7) (1988), 341–360; Math. USSR-Sb., 64:2 (1989), 339–358

Citation in format AMSBIB
\Bibitem{Gur88}
\by R.~I.~Gurielashvili
\paper On the integrability of a~conjugate function in $L^p$ with the polynomial weight
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 136(178)
\issue 3(7)
\pages 341--360
\mathnet{http://mi.mathnet.ru/msb1746}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=959486}
\zmath{https://zbmath.org/?q=an:0677.42008|0665.42014}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 2
\pages 339--358
\crossref{https://doi.org/10.1070/SM1989v064n02ABEH003312}