Tony Nogueira

Optimal constants for a mixed Littlewood type inequality

For

Summability of multilinear forms on classical sequence spaces

p,q\geq2

Optimal Hardy–Littlewood inequalities uniformly bounded by a universal constant

, the Hardy and Littlewood inequalities for real bilinear forms, in its unified formulation, assert that there is a constant

The Bohnenblust–Hille Inequality for Polynomials Whose Monomials have a Uniformly Bounded Number of Variables

C_{p,q}\geq1

Some applications of the Hölder inequality for mixed sums

such that \begin{equation} \left(\sum\limits_{j=1}^{\infty}\left(\sum\limits_{k=1}^{\infty}\left\vert A(e_{j},e_{k})\right\vert ^{2}\right) ^{\frac{\lambda}{2}}\right) ^{\frac {1}{\lambda}}\leq C_{p,q}\left\Vert A\right\Vert, \end{equation} with sharp exponent

On summability of multilinear operators and applications

\lambda=\frac{pq}{pq-p-q},

When are the Hardy-Littlewood inequalities contractive?

for all continuous bilinear forms

Optimal constants for the mixed

A:\ell_{p}\times\ell_{q}\rightarrow\mathbb{R}

\left(\ell_{\frac{p}{p-1}}, \ell_2\right)

(as usual,

-Littlewood inequality

c_{0}