On the Construction of Hölder and Proximal Subderivatives

Xianfu Wang
Simon Fraser University/Centre for Experimental and Constructive Mathematics

ABSTRACT. We construct Lipschitz functions such that for all s>0 they are s-Hölder, and so proximally, subdifferentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitz functions with prescribed Hölder and approximate subderivatives.