U. Goginava

A Counterexample to Belinsky's Conjecture on Ces\`aro Means at Lebesgue Points

In 1997, Belinsky conjectured that, for convex subsequences, the logarithmic growth condition of Carleson, Trigub, and Zagorodni\u{\i} is necessary and sufficient for the arithmetic means of subsequential Fourier partial sums to converge at every Lebesgue point of every integrable function. We disprove the sufficiency...