Resumen de Improved bounds in the scaled Enflo type inequality for Banach spaces
It is shown that if (X; ¿a ¿E ¿aX) is a Banach space with Rademacher type p > 1 then for every n ¿¸ N there exists an even integer m . n2..1=p log n such that for every f : Zn m ¿¨ X, Ex;" [f ( x + m 2 " ) . f(x) p X ] .X mp ¿°n j=1 Ex [ ¿af(x + ej) . f(x)¿ap X ] ;
where the expectation is with respect to uniformly chosen x ¿¸ Zn m and " ¿¸ {.1; 1}n. This improves a bounds of m . n3..2=p that was obtained in [7]. The proof is based on an augmentation of the \smoothing and approximation" scheme, which was implicit in [7].
