Geodesic
A weight space invariant with respect to a singular linear operator
Matematičeskie zametki, Tome 20 (1976) no. 4, pp. 549-558 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{MZM_1976_20_4_a9,
     author = {A. Ya. Yakubov},
     title = {A~weight space invariant with respect to a~singular linear operator},
     journal = {Matemati\v{c}eskie zametki},
     pages = {549--558},
     year = {1976},
     volume = {20},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_4_a9/}
}
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A. Ya. Yakubov. A weight space invariant with respect to a singular linear operator. Matematičeskie zametki, Tome 20 (1976) no. 4, pp. 549-558. http://geodesic.mathdoc.fr/item/MZM_1976_20_4_a9/