Author

D. Núñez-Alarcón

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Preprint Sep 2026

Binary dimension-free discretization and polynomial complexification on real cubes

Let $C(d,2)$ be the optimal dimension-free ratio between the polytorus and Boolean-cube norms of complex multiaffine polynomials of degree at most $d$. For every $d$, $C(d,2)$ equals the unrestricted complexification constant of the real cube for complex polynomials of degree at most $d$. Moreover, $\lim_{d\to\infty}C(...

Luis Miguel Castaño-Marín, D. Núñez-Alarcón, J. Santos · 0 citations

Preprint Sep 2026

The phase diagram of injective-to-projective tensor distortion

For finite-dimensional Banach spaces $E$ and $F$, set \[ \rho(E,F):=\sup_{0\neq z\in E\otimes F}\frac{\pi(z)}{\varepsilon(z)}. \] The square growth of $\rho(\ell_p^d,\ell_q^d)$ was determined by Bonet, Defant, Peris and Ramanujan. We study the rectangular problem with the two dimensions varying independently. If $r=\mi...

D. Núñez-Alarcón, D. Pellegrino, J. Santos · 0 citations

Preprint Aug 2026

Optimality in a Multilinear Extension of Kwapie\'n's Theorem

Bayart, Pellegrino and Rueda proved that every continuous $m$-linear operator from $(\ell_1)^m$ into $\ell_p$ is absolutely $(r_{m,p};1)$-summing, for explicit exponents $r_{m,p}$. The optimality of these exponents was known for $2\le p\le\infty$. We prove optimality in the remaining range $1\le p<2$. Our argument is f...

Luis Miguel Castaño Marín, D. Núñez-Alarcón, Geivison Ribeiro et al. · 0 citations