ThisstudyfocusesontheanisotropicBesov-LionstypespacesBp,θl(Ω;E0,E)associatedwithBanachspacesE0andE.Undercertainconditions,dependingonl=(l1,l2,…,ln)andα=(α1,α2,…,αn),themostregularclassofinterpolationspaceEαbetweenE0andEarefoundsothatthemixeddifferentialoperatorsDαareboundedandcompactfromBp,θl+s(Ω;E0,E)toBp,θs(Ω;Eα).Theseresultsareappliedtoconcretevector-valuedfunctionspacesandtoanisotropicdifferential-operatorequationswithparameterstoobtainconditionsthatguaranteetheuniformBseparabilitywithrespecttotheseparameters.BytheseresultsthemaximalB-regularityforparabolicCauchyproblemisobtained.Theseresultsarealsoappliedtoinfinitesystemsofthequasi-ellipticpartialdifferentialequationsandparabolicCauchyproblemswithparameterstoobtainsufficientconditionsthatensurethesameproperties.
