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

نویسندگان
Munoz-Tello, Andres Felipe ID 1
Delgado Valencia, Julio Cesar ID 2

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

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

doi
10.22075/ijnaa.2021.24089.2667
چکیده

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.

کلیدواژه‌ها
Gateaux differentiability, Norms, Measure