Elements of Singular Integrals

TheSingular integral operator Calderón–Zygmund theoryCalderón–Zygmund singular integral operator of singular integral operators is a very refined mathematical tool whose full power is yet to be exploited (see Stein [140], Meyer [102]). This chapter is devoted to a careful and accessible exposition of the most elementary part of the Calderón–Zygmund theory. We present a straightforward treatment of the Calderón–Zygmund theory necessary for the study of elliptic boundary value problems, assuming only basic knowledge of real analysis and functional analysis. The results discussed here are adapted from Calderón–Zygmund [22–25, 28] and Tanabe [166, 167].