On the set of Gateaux differentiability of the $L^1$ norm

Document Type : Research Paper


1 Universidad del Valle, Departamento de Matematicas, Calle 13 100-00, Cali, Colombia

2 Universidad Santiago de Cali, Calle 5 62-00, Cali, Colombia


Let $(\Omega, \mathcal{M}, \mu)$ be a measure space. In this paper, we establish the set of Gateaux differentiability for the usual norm of $L^{1}(\Omega, \mu)$ and the corresponding derivative formulae at each point in this set.


Volume 14, Issue 1
January 2023
Pages 95-100
  • Receive Date: 27 June 2021
  • Revise Date: 06 August 2021
  • Accept Date: 21 August 2021