Remarks on Remarks on Non Linear Type and Pisier’s Inequality [5]
نویسنده
چکیده
Talagrand showed in [7] that in general the logn factor is necessary. However, the main result of Naor and Schechtman [5] is that a stronger version of the inequality, without the logarithmic factor, holds for UMD spaces, a subclass of Banach spaces that contains in particular all Lp spaces for 1< p <∞. Naor and Schechtman also prove a family of inequalities generalizing Pisier’s inequality. Pisier’s inequality was originally used to relate notions of type and metric type (defined in Section 3). Having strengthened the inequality, Naor and Schechtman go on prove several results that show several different notions of type to be equivalent in the case of UMD spaces, which are summarized in Theorem 3.1.
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تاریخ انتشار 2013