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On bisingular integral operators with discontinuous coefficients

R. V. Duduchava


Abstract: Necessary and sufficient conditions are obtained for bisingular integral operators on piecewise smooth Lyapunov curves with discontinuous coefficients in the $L_p$-spaces with a weight to be Noetherian. The Banach algebra generated by these operators is studied; a regularizer is constructed in the case of continuous coefficients.
Bibliography: 40 titles.

UDC: 517.43

MSC: Primary 47G05; Secondary 47B30, 46L20

Received: 26.02.1975

 English version: Mathematics of the USSR-Sbornik, 1976, 30:4, 515–537

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