room: A1-33, 10:30–12:00

Frédéric Bayart (Clermont Auvergne University, France)
Multiple summing maps: Coordinatewise summability, inclusion theorems and p-Sidon sets

Summary. In 1931, Bohnenblust and Hille have shown the following beautiful inequality which has many applications in the theory of Dirichlet series or in complex analysis: let \(m\geq 1\). There exists a constant \(C_m > 0\) such that, for all m-linear maps \(T\colon c_0 \times\dots\times c_0 \to\mathbb{C}\),
\[
\left(\sum_{i_1,\dots,i_m}\left|T(e_{i_1},\dots,e_{i_m})\right|^{\frac{2m}{m+1}}\right)^{\frac{m+1}{2m}} \leq C_m\|T\|.
\] This inequality may be translated in the modern theory of multiple summing maps. Following works of Defant, Popa and Schwarting, I will discuss in this talk how the arguments used to prove the Bohenblust and Hille inequality can be transfered to this more general context. In particular, we will study the multiple summability of multilinear maps when we have informations on the summability of the maps that it induces in each coordinate. Applications will be given to harmonic analysis.

Coffee and the at 9:00 in the room A1-33.