Lp estimates for the commutators of Marcinkiewicz integrals with kernels belonging to certain block spaces

This paper is devoted to the study of the L-p-mapping properties of the higher order commutators mu(k)(Omega,a), mu(Omega lambda,a)*(,k) and mu(k)(Omega), S,a, which are formed respectively by a BMO(R-n) function a(x) and a class of rough Marcinkiewicz integral operators mu Omega, mu(*)(Omega,lambda), and mu(Omega,S) related to the Littlewood-Paley g-function, the Littlewood-Paley g(lambda)*-function and the Lusin area integral, respectively. By the method of block decomposition for kernel functions and Fourier transforms estimates, some new results about the L-p (R-n) boundedness for theses commutators are obtained. (C) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.