Multilinear Operators And Their Commutators On Weighted Morrey Spaces

The classical Morrey spaces were introduced by Morrey to investigate the local be-havior of solutions to second order elliptic partial differential equations. We know that many properties of solutions to PDE can be attributed to the boundedness of some oper-ators on Morrey spaces. The suitable subspace of the classical Morrey spaces was intro-duced by Vitanza and applied to there to obtain a regularity result for elliptic partial dif-ferential equations. Komori and Shirai defined a weighted Morrey space and investigated the boundedness of classical operators in harmonic analysis, that is, the Hardy-Littlewood maximal operator, the Calderon-Zygmund operator, the fractional integral operator, etc.In this article, we pay attention to the topic of multilinear singular integrals operators and their commutators on weighted Morrey space.In chapter2, we study the iterated commutators for multilinear singular integrals on weighted Morrey spaces and a strong type estimate and a weak endpoint estimate for the commutators are obtained.In chapter3, some multilinear maximal functions and the generalized Calderon-Zygmund operators and their commutators with non-smooth kernels are studied. And also the strong boundedness of these operators are proved on weighted Morrey spaces.In the last chapter, we established strong inequalities of multilinear Fourier multipli-ers and their commutators with Sobolev regularity on weighted Morrey spaces.In the last section of every chapter, some remarks and further results for the respond-ing multilinear operators are discussed.