It is obtained a Zigmund type estimate for the bisingular integral in the space of Summation
functions. It is constructed an invariant functional space based on the inequality. Using the method
of successive approximations it is proven the solvability of the nonlinear bisingular integral equation
in invariant space.
Abdullaev S.K., Babaev A.A. Some
estimates for a singular integral with
summable density. Dokl. Akad. Nauk
SSSR, 188:2(1969), 263-265.
Abdullaev S.K., Babaev A.A. On a
singular integral with summable
density. Func. anal. and appl., Baku,
(1978), 3-32.
Babaev A.A. Some properties of a
singular integral with a continuous
density, and its applications. Dokl.
Akad. Nauk SSSR, 170, 5(1966), 255-
Гусейнов Е.Г. Салаев В.В. Особый
интеграл по отрезку прямой в
пространствах суммируемых
функций. Науч. р. МВ и ССО Азерб.
ССР серия физ.-мат. наук 979) 8 -
Zak I.E. On conjugate double
trigonometric series. Mat.Sb.31,
(1952), 469-484.
Luzin N.N. The Integral and
Trigonometric Series, 2^nded.
Gostekhizdat, Moscow (1951).
Салаев В.В. Некоторые свойства
особого интеграла. Уч. зап. АГУ им.
С.М.Кирова сер. физ.-мат.н. 44
(1966).
Hardy G.H., Littlwood J.E., Polya G.
Inequalities. 2^nd ed. Cambridge
University Press, Cambridge, 1967.
Khvedelidze B. Modern problems of
mathematics. Moscow: "VINITI",
(1975), 5-162.
Холмуродов Э. Некоторые оценки
для особого интеграла с локально
суммируемой плотностью. Уч. зап.
АГУ им. С.М.Кирова сер. физ.-мат.н.
(1978), 71-80.
Jean-Michel Bony. Resolution des
conjectures de Calderon et espaces de
Hardy generalizes. "Asterisque", 92-
(1982), 293-300.
Calderon A.P. Cauchy integrals on
Lipschitz curves and related operators.
Proc. Nat. Acad. Sci. USA, 74(1977),
-1327