Abstract
We describe a recent progress in finding optimal bounds of Hausdorff dimension of singular sets of functions in Lebesgue spaces, Sobolev spaces, Bessel potential spaces, Besov spaces, Lizorkin-Triebel spaces, and Hardy spaces. We are also interested in the question of existence of maximally singular functions in a given space of functions, that is, functions such that the Hausdorff dimension of their singular sets is maximal possible.
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