On Whitney-type extension theorems on Banach spaces for $C^{1,\omega }$, $C^{1,+}$, $C_{\mathrm{loc}}^{1,+}$, and $C_{\mathrm{B}}^{1,+}$-smooth functions

Michal Johanis, Václav Kryštof, Luděk Zajíček

Our paper is a complement to a recent article by D. Azagra and C. Mudarra (2021). We show how older results on semiconvex functions with modulus $\omega$ easily imply extension theorems…