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Characterization of W1(Lloc1(Rd),Tp,α(Rd)) and W1(Lloc1(Rd),Mp,α(Rd))


Domion DOUYON (1) and MOUMINE SANOGO (2) BACARY SAVADOGO (3)
D.E.R Mathématiques et Informatique, Université
BPE 3206 Bamako, Mali


Mathematics Subject Classification: (MSC 2010) 46E35, 46E27, 35A02, 47G40
Key words : amalgam space, Sobolev space, Bounded variation.

Abstract:

In this paper we give a characterization of the spaces  W1(                )
 L1loc(ℝd ),T p,α(ℝd) and  W1(                 )
 L1loc(ℝd ),M  p,α(ℝd) (1 α p ≤∞) in terms of difference quotients smilar to the classical one of  W1(d)  (1 < α ≤∞) and BV (d).

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