Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The sup-norm vs. the norm of the coefficients: equivalence constants for
  homogeneous polynomials   Let $A_{p,r}^m(n)$ be the best constant that fulfills the following
inequality: for every $m$-homogeneous polynomial $P(z) = \sum_{|\alpha|=m}
a_{\alpha} z^{\alpha}$ in $n$ complex variables, $$\big( \sum_{|\alpha|=m}
|a_{\alpha}|^{r} \big)^{1/r} \leq A_{p,r}^m(n) \sup_{z \in B_{\ell_p^n}}
\big|P(z) \big| .$$ For every degree $m$, and a wide range of values of $ p,r
\in [1,\infty]$ (including any $r$ in the case $p \in [1,2]$, and any $r$ and
$p$ for the 2-homogeneous case), we give the correct asymptotic behavior of
these constants as $n$ (the number of variables) tends to infinity. Remarkably,
in many cases, extremal polynomials for these inequalities are not (as
traditionally expected) found using classical random unimodular polynomials,
and special combinatorial configurations of monomials are needed. Namely, we
show that Steiner polynomials (i.e., $m$-homogeneous polynomials such that the
multi-indices corresponding to the nonzero coefficients form partial Steiner
systems), do the work for certain range of values of $p,r$.
  As a byproduct, we present some applications of these estimates to the
interpolation of tensor products of Banach spaces, to the study of (mixed)
unconditionality in spaces of polynomials and to the multivariable von
Neumann's inequality.

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The categories of this paper are: alg-geom
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an