Boundedness Of Parabolic Littlewood-Paley Operator On Triebel-Lizorkin Space

The core of this thesis, which consists of three chapters, mainly studies the boundedness properties of the parabolic Littlewood-Paley operators and their com-mutators on Triebel-Lizorkin spaces.In the chapter1, the boundedness is obtained on homogeneous Triebel-Lizorkin spaces for the parabolic Littlewood-Paley operators with the kernels belonging to the block spaces Bq0,-1/2(Sn-1).In the chapter2, we mainly study the boundedness of the commutators Mb(f)(x) generated by the parabolic Littlewood-Paley operators and BMO functions on homo-geneous Triebel-Lizorkin spaces, where the kernels belonging to the spaces L(log)+L(Sn-1In the chapter3, the boundedness is obtained on homogeneous Triebel-Lizorkin spaces for a class of parabolic Littlewood-Paley operators with kernels belonging to the spaces LilogL)1/γ(Sn-1)(γ≥2).