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Regular subclasses in the Sobolev space

✍ Scribed by Donatella Bongiorno

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
407 KB
Volume
70
Category
Article
ISSN
0362-546X

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✦ Synopsis

We study some slight modifications of the class Ξ±-AC n (Ω, R m ) introduced in [D. Bongiorno, Absolutely continuous functions in R n , J. Math. Anal. and Appl. 303 (2005) 119-134]. In particular we prove that the classes Ξ±-AC n Ξ» (Ω, R m ), 0 < Ξ» < 1, introduced in [C. Di Bari, C. Vetro, A remark on absolutely continuous functions in R n , Rend. Circ. Matem. Palermo 55 (2006) 296-304] are independent by Ξ» and contain properly the class Ξ±-AC n (Ω, R m ).

Moreover we prove that

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