Necessary and sufficient conditions to be Noetherian are obtained for two-dimensional singular integral operators on Lebesgue spaces with a weight coefficient. A formula for calculation of their index is given.

中文翻译：

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有界简单连通域上的Noether条件和一类奇异积分算子的索引

对于带权系数的Lebesgue空间上的二维奇异积分算子，获得了成为Noetherian的充要条件。给出了计算其指数的公式。