The local Hölder function of a continuous function

Abstract This work focuses on the local Holder exponent as a measure of the regularity of a function around a given point. We investigate in detail the structure and the main properties of the local Holder function (i.e., the function that associates to each point its local Holder exponent). We prove that it is possible to construct a continuous function with prescribed local and pointwise Holder functions outside a set of Hausdorff dimension 0.