Modulus and characteristic of convexity: Difference between revisions

Revision as of 06:49, 22 April 2021

Revision as of 18:39, 5 July 2021

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| doi = 10.2307/1969275

| issue = 2

| publisher = Annals of Mathematics

| jstor = 1969275

}}</ref>

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* When ''X'' is uniformly convex, it admits an equivalent norm with power type modulus of convexity.<ref>see {{citation

| last=Pisier |first=Gilles |author-link=Gilles Pisier

| title= Martingales with values in uniformly convex spaces | journal=[[Israel J. Math.]] | volume=20 | year=1975 | issue=3–4 | pages=326–350 | doi = 10.1007/BF02760337 | doi-access=free | mr=394135|s2cid=120947324 }}

.</ref> Namely, there exists {{nowrap|''q'' &ge; 2}} and a constant&nbsp;{{nowrap|''c'' &gt; 0}} such that

::<math>\delta(\varepsilon) \ge c \, \varepsilon^q, \quad \varepsilon \in [0, 2].</math>