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Universally divergent Fourier series via Landau's extremal functions

Gerd Herzog; Peer Chr. Kunstmann — 2015

Commentationes Mathematicae Universitatis Carolinae

We prove the existence of functions $f \in A (𝔻)$ , the Fourier series of which being universally divergent on countable subsets of $𝕋 = \partial 𝔻$ . The proof is based on a uniform estimate of the Taylor polynomials of Landau’s extremal functions on $𝕋 ∖ {1}$ .

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