Geodesic
Convolution integral operators on a~quadrant with discontinuous symbols
Izvestiya. Mathematics , Tome 10 (1976) no. 2, pp. 371-392.

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Necessary and sufficient conditions are obtained for convolution integral operators on a quadrant with discontinuous symbols to be Noetherian in $L_p$-spaces and in Sobolev–Slobodeckii spaces. The algebra generated by these operators is studied, and a regularizer is constructed in the case of continuity of the symbol. Bibliography: 18 titles. 
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R. V. Duduchava. Convolution integral operators on a~quadrant with discontinuous symbols. Izvestiya. Mathematics , Tome 10 (1976) no. 2, pp. 371-392. http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a8/

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