Abstract:We prove the existence of functions $f\in A(\mathbb D)$, the Fourier series of which being universally divergent on countable subsets of $\mathbb T = \partial \mathbb D$. The proof is based on a uniform estimate of the Taylor polynomials of Landau's extremal functions on $\mathbb T\setminus\{1\}$.
Keywords: Fourier series; universal functions; Landau's extremal functions
DOI: DOI 10.14712/1213-7243.2015.115
AMS Subject Classification: 42A16 30B30 47B38