Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W^(m,p)(Ω)  

作　　者：Lijing Zhao Weihua Deng Jan S.Hesthaven 

机构地区：[1]School of Mathematics and Statistics,Northwestern Polytechnical University,Xi'an 710129,China [2]School of Mathematics and Statistics,Gansu Key Laboratory of Applied Mathematics and Complex Systems,Lanzhou University,Lanzhou 730000,China [3]EPFL-SB-MATHICSE-MCSS,Ecole Polytechnique Federale de Lausanne,Lausanne CH-1015,Switzerland

出　　处：《Science China Mathematics》2021年第12期2611-2636,共26页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11801448);the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2018JQ1022).;supported by National Natural Science Foundation of China(Grant No.11271173).

摘　　要：Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena.Although there are extensive numerical methods for solving the corresponding model problems,theoretical analysis such as the regularity result,or the relationship between the left-side and right-side fractional operators is seldom mentioned.Instead of considering the fractional derivative spaces,this paper starts from discussing the image spaces of Riemann-Liouville fractional integrals of L_(p)(Ω) functions,since the fractional derivative operators that are often used are all pseudo-differential.Then the high regularity situation-the image spaces of Riemann-Liouville fractional integral operators on the W^(m,p)(Ω) space is considered.Equivalent characterizations of the defined spaces,as well as those of the intersection of the left-side and right-side spaces are given.The behavior of the functions in the defined spaces at both the nearby boundary point/points and the points in the domain is demonstrated in a clear way.Besides,tempered fractional operators are shown to be reciprocal to the corresponding Riemann-Liouville fractional operators,which is expected to contribute some theoretical support for relevant numerical methods.Last,we also provide some instructions on how to take advantage of the introduced spaces when numerically solving fractional equations.

关 键 词：image space Riemann-Liouville integral regularity property APPROXIMATION 

分 类 号：O177.6[理学—数学]