On translation invariant singular integral operators

In this thesis, we give a first introduction to the theory of singular integral operators on R^n. These operators arise naturally in the regularity study of elliptic and parabolic equations. We will first study the case of translation invariant singular integral operators, which can be described by a multiplication operatör on the Fourier transform side. While the continuity on L^2 (R^n ) easily follows from Plancherel' s theorem, the proof of continuity on〖 L〗^p (R^n ) for 1Keyword: Hardy uzayı = Hardy space ; Riesz dönüşümü = Riesz transformation