The Boundedness of Singular Integral Operator along an Open Curve

It is well known that, the singular integral operator S defined as:if L is a closed smooth contour in the complex plane C, then S is a bounded linear operator from H(L) into H(L); if L Is an open smooth curve, then S is Just a linear operator from H into H. In this paper, we define a Banach space H , and prove that S: H-H, is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators.