Multifractal analysis of the divergence of Fourier series: the extreme cases

Abstract

We study the size, in terms of the Hausdorff dimension, of the subsets of $\mathbb{T}$ such that the Fourier series of a generic function in $L^1(\TT)$, $L^p(\TT)$ or in $\mathcal{C}(\mathbb{T})$ may behave badly. Genericity is related to the Baire category theorem or to the notion of prevalence.

Cited by in corpus (1)

• Multifractal spectra of typical and prevalent measures