Singular Integrals
نویسنده
چکیده
In this paper I will a t tempt to describe the subject as it has developed in the last fifteen years, outlining the methods by which its problems have been approached and discussing its connections with other branches of Analysis. I t will perhaps be best to start by considering certain classical situations which lead naturally to singular integrals and which contain the seeds of some of the methods and some of the applications we will discuss later. The simplest one arises in attempting to establish the connection between the real and imaginary parts of the boundary values of an analytic function. Suppose tha t ƒ (z) is analytic in Iiz) ^ 0 and that zf(z) is bounded, then if u(x) and v(x) are the real and imaginary parts of ƒ on R(z) = 0, we have
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