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U. Goginava

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Preprint Aug 2026

Cesaro Means along Polynomial Subsequences of Fourier Partial Sums at Lebesgue Points

In 1936, Zalcwasser proved the almost everywhere convergence of the arithmetic means of the square subsequence of trigonometric Fourier partial sums and asked whether this result extends to higher powers and to Ces\`aro means of fractional order. We give affirmative answers to both questions in a stronger pointwise for...

U. Goginava · 1 citation

Preprint Aug 2026

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...

U. Goginava · 0 citations