This paper is primarily concerned with the proof of the Lp boundedness of parabolic Littlewood-Paley operators with kernels belonging to certain block spaces. Some known results are essentially extended and improved.
In this note, the authors prove that the commutator Tb, generated by θ-type Calderon-Zygmund operator T and a Lipschitz function b is bounded from LP（R^n） intoLip（β_n/p）（R^n） and also maps from Ln/β （R^n） into BMO（R^n）.
