On generalizations of Gowers norms and their geometry
msra(2009)
摘要
Motivated by the definition of the Gowers uniformity norms, we introduce and
study a wide class of norms. Our aim is to establish them as a natural
generalization of the $L_p$ norms. We shall prove that these normed spaces
share many of the nice properties of the $L_p$ spaces. Some examples of these
norms are $L_p$ norms, trace norms $S_p$ when $p$ is an even integer, and
Gowers uniformity norms.
Every such norm is defined through a pair of weighted hypergraphs. In regard
to a question of Laszlo Lovasz, we prove several results in the direction of
characterizing all hypergraph pairs that correspond to norms.
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关键词
uniform convexity.,uniform smoothness,hypergraphs,gowers norms,graph densities,normed space,functional analysis
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