| It is well known that harmonic analysis has become one of the key research areas of modern mathematics, and is widely used in partial differential equations. Calderon-Zygmund theory as a key theory appeared in modern harmonic analysis. Since the nine-teen nineties, Calderon-Zygmund theory has been attracted by many mathematicians on function spaces with nondoubling measures, and a lot of classical results were extended to these function spaces. Recently, a so-called metric measure space was introduced with the properties of geometrically doubling and upper doubling. It generalizes the Calderon-Zygmund theory. We will study the boundedness of some multilinear operators on the Morrey space with nondoubling measures. The details are listed as follows.In the second section, we prove that the parametric gλ*functions and parametric Marcinkiewicz integrals Mλ*p are bounded on Mqp(k,μ) with suitable indexes p and A and for all1<q≤p<∞.In the following section, we obtained the boundedness of the iterated commutator from Mq1p1(μ)×…×Mqmpm(μ to Mqp(μ) with1<qj≤pj<∞,1/p=1/lP1+…+1/pm,1/q=1/q1+…+1/qm, which generated by the multilinear Carlderon-Zygmund operators and the symbols b∈RBMO(μ)m.We postpone the results of multilinear fractional integrals and their commutator to the last section, that if1<qi≤pi<∞,0<α<m,1/p=1/p1+…1+/pm-α>0, b∈RBMOm, then Tm.α and [b, Tm.α] are bounded from Mq1p1(X,μ)×…×Mqmpm(X,μ) to M qp(X,μ). |
