Research On Boundedness Of Some Multi(Sub)Linear Operators On Function Spaces

This dissertation is devoted to the boundedness of some multi(sub)linear operators such as the multi(sub)linear John-Stromberg local maximal operator, the commutators generated by BMO(Rn) functions and the bilinear Fourier multiplier operators and the multilinear Calderon-Zygmund operators. The main results are as follows:1. Chapter2mainly deals with some characterizations of the weights w1,...,wm, for which the multi(sub)linear John-Stromberg local maximal operator M0,s is bounded from Lp1(Rn,w1)×,...,×Lpm(Rm,wm)to Lp(Rn,vW),with p1,...,pm∈(0,∞),p∈(0,∞)and1/In addition, the new characterizations of A∞weight and the weight w which satisfies wθ∈A∞for some θ∈(0,∞), are also obtained.2. The main purpose of Chapter3is to consider the mapping properties on Lp1,(Rn)×LP2(Rn)(p1,p2∈(1,∞)), on H1(Rn)×Lp2(Rn)(p2∈[2,∞)), and on H1(Rn)×H1(Rn) for the commutators generated by BMI(Rn) functions and the bilinear Fourier multiplier operator. It is proved that these mapping properties for the commutators are similar to those of the bilinear Fourier multiplier operators which were established by Miyachi and Tomita.3. Chapter4is concerned with the behaviors on products of weighted Morrey spaces for multilinear Calderon-Zygmund operators with multiple weights. Let T be the m-linear Calderon-Zygmund operator. It is proved that if κ∈(0,1), p1,...,pm∈[1,∞) and then for any T is bounded from Mp1,κ(Rn,w1)×...×Mpi,κ(Rn,wm) to WMp,κ(Rn,vw), where WMp,κ(Rn,w) is the weak weighted Morrey space and the multiple weights Ap were firstly introducted by Lerner.et.al. Moreover, when min1≤k≤m{Pk}>1, then T is bounded from Mp1,κ(Rn,w1)×...×Mpm,κ(Rn,wm) to Mp,κ(Rn,Vw), where Mp,κ(Rn,w) is the weighted Morrey space.