Sums of norm spheres are norm shells and lower triangle inequalities are sharp

2008/05/02 by Mattner, Lutz
#26D99 #46B99 #60E15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.0805.0314

Abstract

The statements in the title are explained and proved, as a little exercise in elementary normed vector space theory at the level of Chapter 5 of Dieudonné's "Foundations of Mathematical Analysis". A connection to recent moment bounds for submartingales is sketched.

Related

• Discrete norming inequalities on sections of sphere, ball and torus
• Khinchin inequalities for uniforms on spheres with a deficit
• Multidimensional probability inequalities via spherical symmetry
• Small cap decoupling inequalities: Bilinear methods
• Strengthened inequalities for the mean width and the ℓ-norm of origin symmetric convex bodies