Boundedness For A Class Of Marcinkiewicz Integral Operators And Its Commutators

In this dissertation, the boundedness for Marcinkiewicz integral operators and its commutators are considered.In the first chapter, we obtain the boundedness for Marcinkiewicz integral operator, which related to the Littlewood-Paley g-function, on the spaces of BMO_w and (BMO)_w. Here w is a weight.In the second chapter, we consider the parametric Marcinkiewicz integral μ_Ω~ρ. If Ω is a homogeneous function of degree zero and satisfies a class of Dini's condition, then the operator μ_Ω~ρ is of strong type (p, p) and weak type (1,1) .In the third chapter, we prove the boundedness of commutator, which generated by the Marcinkiewicz integral and the function 6, on the classical Hardy space and the Herz-type Hardy space.Triebel-Lizorkin space is a very important space in Harmonic Analysis. In the last chapter, we will discuss the boundedness of the commutator [6, T], which generated by the θ-type Calderon-Zygmund operator T and the function b ∈ Λβ . Here the kernel function θ must satisfies some conditions.