ON CONTINUITY OF SINGULAR INTEGRAL-OPERATORS IN SOBOLEV SPACES

In this paper we give conditions for the boundedness of a singular integral operator, acting from the Sobolev class H-m(R(n)) into H-l(R(n)) with m greater than or equal to l greater than or equal to 0. The symbol may depend not only on the angular variable theta is an element of S-n-1 but also on the space variable x is an element of R(n). It will be shown that the conditions, which are stated in terms of a certain space of multipliers, are precise in a sense.