The Study On Boundedness For Multilinear Commutator Of Pseudo-differential Operators

In this paper, we study the boundedness for the multilinear commutator ofpseudo-di-erential operators with BMO function, Lipschitzon function and weightedLipschitzon function on Lp space (1 < p <∞), L~∞(ω) space (ω∈A1) and Bp(ω)space (1 < p <∞,ω∈A1) and all kinds of function estimate.About the multilinear commutator of pseudo-di-erential operators with BMOfunction, we obtain the the boundedness from Lp(Rn) to Lp(Rn)(1 < p <∞), fromL~∞(ω) to BMO(ω) (ω∈A1) and from Bp(ω) to CMO(ω)(1 < p <∞,ω∈A1)respectively.About the multilinear commutator of pseudo-di-erential operators with Lipschitzfunction, we obtain the boundedness from Lp(Rn) to F-pmβ,∞(Rn) (0 <β< m(11-a), 1 <p <∞) and from Lp(Rn) to Lq(Rn) (1 < p <∞, 1q = p1 - mnβ) respectively.About the multilinear commutator of pseudo-di-erential operators with weightedLipschitz function, we obtain the boundedness from Lp(ω) to Lq(ω1-m+(q-1n) mβ) (0 <β< m(11-a),1 < p <∞, 1q = p1 - mnβ,ω∈A1) and from Lp(ω) to F-pmβ,∞(ω1-m-mnβ)(0 <β< m(11-a), 1 < p <∞,ω∈A1,ω-1∈A1) respectively.