Global representation of some mixed ultradistributions

Abstract

Given non empty open subsets $\Omega$ of $\mathbb{R}^r$ and $\Omega'$ of $\mathbb{R}^s$, and sequences $\mathscr{M}$ and $\mathscr{M}'$, we recall the definition of the space ${\mathscr{D}^{\{\mathscr{M},\mathscr{M}'\}}{(\Omega \times \Omega')}}$. Given $p \in [1,+\infty[$, we also introduce the space $\mathscr{D}_{(L^p)}^{\{\mathscr{M},\mathscr{M}'\}}{(\Omega \times \Omega')}$. By use of a basic idea due to Valdivia, we obtain a global representation of the corresponding ultradistributions, i.e. of the elements of the topological duals of these spaces.