Explicit formulas for $C^{1,1}$ and $C_{\text{conv}}^{1,\omega }$ extensions of $1$-jets in Hilbert and superreflexive spaces

Daniel Azagra, Erwan Le Gruyer, Carlos Mudarra

Given $X$ a Hilbert space, $\omega$ a modulus of continuity, $E$ an arbitrary subset of $X$, and functions $f:E\to \mathbb{R}$, $G:E\to X$, we provide necessary and sufficient conditions…