The Boundedness Of Schr?dinger-type Operators With Definite Potential And Their Commutators On L^p(·) (Rⁿ)

Firstly,the definitions and basic properties of the variable exponent Lebesgue spaces and the Schr?dinger type operators,and some applications were introduced.Afterwards,based on the boundedness of the Schr?dinger type operators with certain potential and the commutators of them on classical Lebesgue spaces,by using the Hardy-Littlewood maximal operator is bounded on the variable exponent Lebesgue spaces as well as the properties of the sharp function and the potential (1,the H¨older inequality,the reverse H¨older inequality,the boundedness of the Schr?dinger operators with certain potential on variable Lebesgue spaces was obtained.Furthermore,the boundedness of commutators generated by some Schr?dinger operators and BMO functions [b,T] on variable Lebesgue spaces was proved.