On Hölder continuity and $p^{\mathrm{th}}$-variation function of Weierstrass-type functions

Abstract

We study Hölder continuity, $p^{\mathrm{th}}$-variation function and Riesz variation of Weierstrass-type functions along the sequence of $b$-adic partitions, where $b>1$ is an integer. By a Weierstrass-type function, we mean that in the definition of the well-known Weierstrass function, the power function is replaced by a submultiplicative function, and the Lipschitz continuous cosine and sine functions are replaced by a general periodic Hölder continuous function.

35 pages