arXiv subjects
Publications and source records attributed to Mariana Maia.
We prove a general factorization theorem for Lipschitz summing operators in the context of metric spaces which recovers several linear and nonlinear factorization theorems that have been proved recently in different environments. New applications are also given.
In 2015, using an innovative technique, Carando, Defant and Sevilla-Peris succeeded in proving a Bohnenblust--Hille type inequality with constants of polynomial growth in $m$ for a certain family of complex $m$-homogeneous polynomials. In the present paper, using a completely different approach, we prove that the constants of this inequality are uniformly bounded irrespectively of the value of $m$.
It is well-known that the optimal constant of the bilinear Bohnenblust--Hille inequality (i.e., Littlewood's $4/3$ inequality) is obtained by interpolating the bilinear mixed $\left( \ell _{1},\ell_{2}\right) $-Littlewood inequalities. We remark that this cannot be extended to the $3$-linear case and, in the opposite direction, we show that the asymptotic growth of the constants of the $m$-linear Bohnenblust--Hille inequality is the same of the constants of the mixed $\left( \ell _{\frac{2m+2}{m+2}},\ell _{2}\right) $-Littlewood inequality. This means that, contrary to what the previous works seem to suggest, interpolation does not play a crucial role in the search of the exact asymptotic growth of the constants of the Bohnenblust--Hille inequality. In the final section we use mixed Littlewood type inequalities to obtain the optimal cotype constants of certain sequence spaces.