Resumen de Differentiability and best local approximation

Hector H. Cuenya, Claudia N. Rodriguez

• In this paper we give sufficient conditions over the differentiability of a function to assure existence of the best local approximant in Lp-spaces, 0 < p ≤ ∞. These conditions are weaker than those given in previous papers. For p = 2 we show that, in a certain way, they are also necessary. In addition, we characterize the best local approximant.