March 2025
| Intervenant : | Giorgi Oniani |
| Institution : | School of Mathematics, Kutaisi International University, Kutaisi, Georgia |
| Heure : | 14h00 - 15h00 |
| Lieu : | Bâtiment 307, salle 2L8 |
It will be discussed the following topics: Antonov-Sjölin-Soria type extrapolation in the setting of locally compact groups and its application to a.e. convergence of Vilenkin-Fourier series; Konyagin's problem on a.e. convergence of sub-sequences of Walsh-Fourier sums; Kanznelson's type theorems for sets of divergence of Fourier series in systems of characters for compact Abelian groups; multi-parameter version of Stein's weak type maximal principle and its applications for multiple Fourier series and ergodic averages.
The presentation is based on the papers [1-4] of the author.
References
[1] On Sjölin–Soria–Antonov type extrapolation for locally compact groups and a.e. conver- gence of Vilenkin–Fourier series, Acta Math. Hungar. 163 (2021), No. 2, 429-436.
[2] On the divergence of subsequences of partial Walsh-Fourier sums, J. Math. Anal. Appl. 497 (2021), No. 2, 124900 (joint with U. Goginava).
[3] On the divergence sets of Fourier series in systems of characters of compact Abelian groups, Math. Notes 112 (2022), No. 1, 100–108.
[4] Almost everywhere convergence of nets of operators and weak type maximal inequalities, Fund. Math. 262 (2023), No. 3, 287-304.