thanks!

]]>Cauchy-Schwarz bounds by the geometric mean of and .

]]>Maybe the left side should be squared?

*[Corrected, thanks – T.],*

whenever is real-valued.

]]>Any help?

]]>For all but about of the choices of n (the choices that are closest to the boundary of , the inner average is equal to .

]]>Regarding as representing polynomials in one variable of degree less than n is very natural, but we can have other versions, e.g., polynomials of degree 2 in some m variables (or “bipartite” polynomials of degree 2) , which may make sense over as well. In particular, it will be nice to have cupset versions related to versions of polynomial HJT that Tim Gowers considered here http://gowers.wordpress.com/2009/11/14/the-first-unknown-case-of-polynomial-dhj/ .

]]>Never mind, I got it… Once you assume that the infimum is delta0 > 0, you define f(x) = x+cx^3, with c the value that satisfies (1) for that particular delta0 value (so, yes, a unique value for c). Than f is of course increasing and continuous, and everything else follows… I was thinking in a different way, but your explanation was perfect. Thanks!

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