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Mat. Zametki, 1976, Volume 20, Issue 4, Pages 549–558 (Mi mz7877)  

A weight space invariant with respect to a singular linear operator

A. Ya. Yakubov

Daghestan Polytechnical University

Abstract: For the singular operator
$$ S_u=\int_a^b\frac{K(x,s)u(s)}{s-x} ds $$
invariant weight spaces $\lambda_{\alpha,p}^\beta$ ($u(x)\in\lambda_{\alpha,p}^\beta$ if $1^0$$u(x)\rho(x)\in H_\beta^0$, $2^0$$\|u\|_{L_p(\rho_0)}<\infty$, $\rho(x)=(x-a)(b-x)^{1+\beta}$, $\rho_0(x)-(b-x)^{\alpha(p-1)}$, $0<\alpha$, $\beta<1$, $p>1$, $H_\beta^0$ is a Hölder space. Multiplicative inequalities of the type of Kh. Sh. Mukhtarov are also obtained.

Full text: PDF file (526 kB)

English version:
Mathematical Notes, 1976, 20:4, 864–870

Bibliographic databases:

UDC: 517.5
Received: 06.03.1975

Citation: A. Ya. Yakubov, “A weight space invariant with respect to a singular linear operator”, Mat. Zametki, 20:4 (1976), 549–558; Math. Notes, 20:4 (1976), 864–870

Citation in format AMSBIB
\Bibitem{Yak76}
\by A.~Ya.~Yakubov
\paper A~weight space invariant with respect to a~singular linear operator
\jour Mat. Zametki
\yr 1976
\vol 20
\issue 4
\pages 549--558
\mathnet{http://mi.mathnet.ru/mz7877}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=428113}
\zmath{https://zbmath.org/?q=an:0357.46036}
\transl
\jour Math. Notes
\yr 1976
\vol 20
\issue 4
\pages 864--870
\crossref{https://doi.org/10.1007/BF01098904}


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