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Assouad and Lower Dimensions of Graphs of Weierstrass-Type Functions with Rapidly Growing Frequencies
We study the Assouad and lower dimensions of graphs of Weierstrass-type functions of the form \[ f(x)=\sum_{n=1}^{\infty}a_nϕ(b_nx+θ_n), \qquad x\in\mathbb R, \] where $ϕ$ is a nonconstant $C^2$ function of period one, $a_n,b_n>0$, $(θ_n)$ is an arbitrary sequence of real numbers, $\
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