Annales Mathématiques Africaines

Characterization of W¹(L_loc¹(R^d),T^p,α(R^d)) and W¹(L_loc¹(R^d),M^p,α(R^d))

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 and  W¹ (1 ≤ α ≤ p ≤∞) in terms of difference quotients smilar to the classical one of  W^1,α(ℝ^d)  (1 < α ≤∞) and BV (ℝ^d).