Regular subclasses in the Sobolev space View the MathML sourceWloc1,n

We study some slight modifications of the class αα-ACn(Ω,Rm)ACn(Ω,Rm) introduced in [D. Bongiorno, Absolutely continuous functions in RnRn, J. Math. Anal. and Appl. 303 (2005) 119–134]. In particular we prove that the classes αα-View the MathML sourceACλn(Ω,Rm), 0<λ<10<λ<1, introduced in [C. Di Bari, C. Vetro, A remark on absolutely continuous functions in RnRn, Rend. Circ. Matem. Palermo 55 (2006) 296–304] are independent by λλ and contain properly the class αα-ACn(Ω,Rm)ACn(Ω,Rm). Moreover we prove that View the MathML sourceα-ACn(Ω,Rm)=(α-ACλn(Ω,Rm))∩(α-ACn,λ(Ω,Rm)), Turn MathJax on where αα-ACn,λ(Ω,Rm)ACn,λ(Ω,Rm) is the symmetric class of αα-View the MathML sourceACλn(Ω,Rm), 0<λ<10<λ<1.