Some Operators On Non-homogeneous Metric Measure Spaces

In this dissertation, we shall mainly study the boundedness of some operators on the nonhomogeneous metric measure spaces. The main results are as follows.In section 1, the inequality of type （L^p（μ）, L^q（μ））（1<p<n/β） is established for the Marcinkiewicz commutator M_b generated by the Marcinkiewicz integral operator M and the Lip_μ function b at first. Secondly, the inequality of type （L¹（μ））, L^n/n-β,∞（μ）) is proved for commutator M_b as p=1. And for p=n/B,M_b is a bounded operator from Lp（μ） space into the space RBMO（μ）. Finally, with the aid of the methods of the function decompositions, the boundenness of the commutator M_b is obtained from Hardy spaces H¹（μ） into the spaces L^n/n-β（μ）.In section 2, the boundedness of Marcinkiewicz commutator M_b generated by the Marcinkiewicz integral operator M and the Lip_β（μ） function b is discussed on the Morrey spaces. Meanwhile, it is obtained that M_b is a bounded operator from M_q^n/β（μ） to RBMO（μ）.In section 3, the boundedness of Calderón-Zygmund operators and its commu-tators generated by Lipschitz and RBMO（μ） functions are researched on Morrey spaces over the nonhomogeneous metric measure spaces.