arXiv subjects

Luis Miguel Castaño-Marín

Publications and source records attributed to Luis Miguel Castaño-Marín.

2 recordsLinked to original sources

arXiv2026

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, $\lim_{d\to\infty}C(d,2)^{1/d}=1+\sqrt2$, and for every $d\ge3$, $β(1-6/(5d))(1+\sqrt2)^d\le C(d,2)\le(1+\sqrt2)^d$, where $β=15π/[2(5\sqrt{26}+\log(5+\sqrt{26}))]=0.8473222863\ldots$.

math.FA↗

arXiv2026

Optimality in a Multilinear Extension of Kwapień's Theorem

Bayart, Pellegrino, and Rueda obtained diagonal absolute summability exponents for continuous $m$-linear operators from $(\ell_1)^m$ into $\ell_p$. Their optimality was known for $2\le p\le\infty$, whereas the case $1\le p<2$ remained open. We settle the latter case by means of finite Walsh test operators, and consequently obtain the optimal exponent for every $1\le p\le\infty$. The same argument, combined with the corresponding interpolation and embedding results, also yields optimal Kwapień-type statements for several related range spaces.

math.FA↗