# Multiple summing mpas : coordinatewise summability, inclusion theorems and p-Sidon sets

## TL;DR

This paper investigates the conditions under which multilinear maps are multiple summing based on coordinatewise summability, with applications to inclusion theorems and p-Sidon sets.

## Contribution

It introduces new results linking coordinatewise summability to the multiple summability of multilinear maps and explores their implications for inclusion theorems and p-Sidon sets.

## Key findings

- Established criteria for multiple summing multilinear maps based on coordinatewise properties
- Derived new inclusion theorems for multiple summing multilinear mappings
- Applied results to the study of products of p-Sidon sets

## Abstract

We discuss the multiple summability of a multilinear map $T:X_1\times\cdots\times X_m\to Y$ when we have informations on the summability of the maps it induces on each coordinate. Our methods have applications to inclusion theorems for multiple summing multilinear mappings and to the product of $p$-Sidon sets.