Weighted Boundedness Of Some Fractional Integral Operators And Commutators

Harmonic analysis is one of the core research fields in modern mathematics, the ideas and methods in almost every branch of mathematics. Fractional integral operator has the profound background of partial differential equations, which is an important operators in harmonic analysis. In recent years, about the boundedness of fractional integral operators, multilinear fractional integral operators and commutators on the Euclid spaces obtain many conclusions. This paper mainly discusses the weighted boundedness of fractional integral operators, multilinear commutators of fractional integral operators with rough kernel and multilinear fractional integral commutators. The main contents of this paper are as follows:In chapter 1, we introduces the main content of this research background and status of this paper.In chapter 2, we use the exising results and study skills, discussed fractional integral operators, generalized fractional integral operators and (θ, N)-type fractional integral op-erators on the weighted homogeneous Morrey-Herz spaces MK(p,q)(α,λ)(Rn) is bounded. Our results enriched theory of fractional integral operators.In chapter 3, for b→ ∈ BMOm or b→ ∈ ΛB, we discussed the boundedness of fractional integral operators with rough kernel TΩα with functions b generated commutators TΩαb→ a on the wighted Morrey spaces.In chapter 4, we discussed the boundedness of multilinear fractional integral oper-ators Iα,m with functions b generated commutators I(α,m)(Ⅱb→) and I(α,m)(∑b→) on the weighted Morrey spaces.