Singular integral operators with homogeneous kernels play an important role in harmonic analysis. Their applications spread over many areas of mathematics such as partial differential equations, potential theory and complex analysis. In this thesis, we study a class of singular integral operators in the forin Tof(x) = p. – B(lyly). Powym dy. JRM In this work, we shall present and analyze the theory introduced by Duoandikoetxea and Rubio de Francia in (11]. Also, we prove LP boundedness of such integral operators when their kernels are in certain block spaces, and the mappings are more general than polynomials and convex functions.