The permanence of $mathcal{R}$-boundedness and property($alpha$) under interpolation and applications to parabolic systems

Journal of Mathematical Sciences

Kaip, Mario¹ 

关键词: Interpolation;    $mathcal{R}$-boundedness;    maximal regularity;    parabolic systemS;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Thisnoteconsistsoftwoparts.Inthefirstpartweconsiderthebehaviorof$mathcal{R}$-boundedness,$mathcal{R}$-sectoriality,andproperty($alpha$)undertheinterpolationofBanachspaces.Inageneralsettingweprovethatforinterpolationfunctorsoftype$h$the$mathcal{R}$-boundedness,the$mathcal{R}$-sectoriality,andtheproperty($alpha$)preserveunderinterpolation.Inparticular,thisistrueforthestandardrealandcomplexinterpolationmethods.(Partly,theseresultswereindicatedincite{kalton06},however,withjustaverybriefoutlineoftheirproofs.)Thesecondpartrepresentsanapplicationofthefirstpart.Weprove$mathcalR$-sectoriality,orequivalently,maximal$L^p$-regularityforageneralclassofparabolicsystemsoninterpolationspacesincludingscalesofBesov-andBessel-potentialspacesover$R^n$.

【 授权许可】

Unknown