This article is cited in 1 paper

On a class of singular integral operators with kernels of polar-logarithmic type

N. L. Vasilevskii


Abstract: Integral operators with polar-logarithmic kernels which arise in connection with a problem of F. D. Gahov are studied in the space $L_p(\mathscr L)$. Necessary and sufficient conditions that the operator be Noetherian and a formula for the index of the operators are obtained. A complete solution of Gahov's problem is obtained.
Bibliography: 10 titles.

UDC: 517.948

MSC: Primary 47G05; Secondary 30A88

Received: 19.04.1974

 English version: Mathematics of the USSR-Izvestiya, 1976, 10:1, 127–143

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