Research About Littlewood-Paley Operation And Its Commutator

The disseration is devoted to the boundedness of the Lusin-area integralμΩ,S and gλ*function on the generalized local Morrey space,as well as the boundedness of the commutators generated by μΩ,S or gλ*and local Campanato functions,respectively.The plan is as follows:In Chapter 1,we introduced the background and some related theories to the paper.These involved in Littlewood-Paley Lusin-area integral μΩ,S and its commutator;gλ*function and its commutator;the main content of this paper.In Chapter 2,when Ω∈Ls(Sn-1)(1<s ≤ ∞),applying the properties of the kernel function and the boundedness of μΩ,S on Lp(Rn),we obtain the boundedness of μΩ,s on generalized local Morrey spaces.And,applying the boundedness of μΩ,S on Lp(Rn)and the properties of local Campanato func-tions,we investigate the boundedness of the commutator generated by μΩ,S and local Campanato functions on generalized local Morrey spaces.In Chapter 3,when Ω∈Ls(Sn-1)(1<s ≤ ∞),applying the properties of the kernel function and the boundedness of gλ*function on Lp(Rn),we de-duce the boundedness of gλt function on generalized local Morrey spaces.And,applying the boundedness of gλ*function on Lp(Rn)and the properties of local Campanato functions,we study the boundedness of the commutator generat-ed by gλ*function and local Campanato functions on generalized local Morrey spaces.