In this paper we give conditions for the boundedness of a singular integral operator, acting from the Sobolev class Hm(R") into H'(W) with m~I~0. The symbol may depend not only on the angular variable 9eS"~l but also on the space variable x e R". It will be shown that the conditions, which are stated in terms of a certain space of multipliers, are precise in a sense.
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