Author

A. Barbosa

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Preprint Oct 2026

Polynomial Bohnenblust--Hille Bounds and Hardy--Littlewood Inequalities for Finite Local Systems

The complex polynomial Bohnenblust--Hille inequality states that, for a $d$-homogeneous polynomial $P:\mathbb C^N\to\mathbb C$, $P(z)=\sum_{|\alpha|=d}c_\alpha z^\alpha$, the coefficient norm $(\sum_{|\alpha|=d}|c_\alpha|^{p_d})^{1/p_d}$ is bounded by $B_d^{\mathrm{pol}}\|P\|_\infty$, where $p_d=2d/(d+1)$ and $B_d^{\ma...

A. Barbosa, D. Núñez-Alarcón, D. Pellegrino et al. · 0 citations

Preprint Oct 2026

Sparse Kahane--Salem--Zygmund Forms and Weighted Hardy--Littlewood Inequalities Across the Critical Endpoint

We study sparse Kahane--Salem--Zygmund constructions and weighted Hardy--Littlewood inequalities for homogeneous polynomials. For supports of cardinality $n^{d+o(1)}$, we determine the sharp power of $n$ governing the smallest norm of a unimodular $m$-linear form on $\ell_{p_1}^n\times\cdots\times\ell_{p_m}^n$; in the...

A. Barbosa, D. Núñez-Alarcón, A. Raposo et al. · 0 citations

Preprint Sep 2026

The Lotz Property in Weakly Compactly Generated Spaces

We study whether every infinite-dimensional weakly compactly generated (WCG) Banach space fails the Lotz property. The answer is affirmative in the nonseparable case: a classical decomposition theorem for WCG spaces provides a Schauder decomposition, and an explicit diagonal $C_0$-semigroup has an unbounded generator....

G. Ara'ujo, Mateus Azevedo, Flank Bezerra et al. · 0 citations