Improved bounds in the scaled Enflo type inequality for Banach spaces

• Autores: O. Giladi, Assaf Naor
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 25, Nº 2, 2010, págs. 151-164
• Idioma: inglés
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• Resumen

  • 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].