Polona Durcik
Publications and preprints
Link to arxiv.
(with K. Domelevo, V. Fragkiadaki, O. Klein, D. Oliveira e Silva, L. Slavíková, B. Wróbel) Dimension-free inequalities for low and high degree functions on the Hamming cube, submitted. 2401.07699
(with L. Slavíková, C. Thiele) Norm-variation of triple ergodic averages for commuting transformations, submitted. 2307.07372
(with V. Kovač, M. Stipčić) A strong-type Furstenberg-Sárközy theorem for sets of positive measure, J. Geom. Anal. 33 (2023), issue 8, article no. 255, 16 pp. 2302.13548
(with J. Roos) A new proof of an inequality of Bourgain, To appear in Math. Res. Lett. 2210.01326
(with M. Stipčić) Quantitative bounds for products of simplices in subsets of the unit cube, To appear in Isr. J. Math. 2206.10004.
(with L. Slavíková, C. Thiele) Local bounds for singular Brascamp-Lieb forms with cubical structure, Math. Z. 302 (2022), 2375-2405. 2112.15101.
(with R. Greenfeld, A. Iseli, A. Jamenshan, J. Madrid) An uncountable ergodic Roth theorem and applications, Discrete Contin. Dyn. Syst., 42(11) (2022), 5509-5540. 2101.00685.
(with M. Christ, V. Kovač, J. Roos) Pointwise convergence of certain continuous-time double ergodic averages, Ergodic Theory Dynam. Systems. 42 (2022), no. 7, 2270-2280. 2011.06370.
(with M. Christ, J. Roos) Trilinear smoothing inequalities and a variant of the triangular Hilbert transform, Adv. Math. 390 (2021), Paper No. 107863. 2008.10140.
(with F. Bernicot) Boundedness of some multi-parameter fiber-wise multiplier operators, Indiana Univ. Math. J. (2020). 2007.02211.
(with V. Kovač) A Szemerédi-type theorem for subsets of the unit cube, Anal. PDE. 15 (2022), no. 2, 507-549. 2003.01189.
(with L. Cladek, B. Krause, J. Madrid) Directional maximal function along the primes, Publ. Mat. 65 (2021), no. 2, 841–858. 1909.13319.
(with C. Thiele) Singular Brascamp-Lieb: a survey, Geometric Aspects of Harmonic Analysis, Vol. 45, Springer INdAM Series, Springer International Publishing, 2021. 1904.08844.
(with J. Roos) Averages of simplex Hilbert transforms, Proc. Amer. Math. Soc. 149 (2021), no. 2, 633-647. 1812.11701.
(with V. Kovač) Boxes, extended boxes, and sets of positive upper density in the Euclidean space, Math. Proc. Cambridge Philos. Soc., 171 (2021), no. 3, 481–501. 1809.08692.
(with C. Thiele) Singular Brascamp-Lieb inequalities with cubical structure, Bull. London Math. Soc. 52 (2020), no. 2, 283–298. 1809.08688.
(with S. Guo, J. Roos) A polynomial Roth theorem on the real line, Trans. Amer. Math. Soc. 371 (2019), no. 10, 6973-6993. 1704.01546.
(with V. Kovač, L. Rimanić) On side lengths of corners in positive density subsets of the Euclidean space, Int. Math. Res. Not. 2018, no. 22, 6844-6869. 1609.09056.
(with V. Kovač, C. Thiele) Power-type cancellation for the simplex Hilbert transform, J. Anal. Math. 139 (2019), 67–82. 1608.00156.
(with V. Kovač, K. A. Škreb, C. Thiele) Norm-variation of ergodic averages with respect to two commuting transformations, Ergodic Theory Dynam. Systems 39 (2019), no. 3, 658-688. 1603.00631.
Lp estimates for a singular entangled quadrilinear form, Trans. Amer. Math. Soc. 369 (2017), no. 10, 6935-6951. 1506.08150.
An L4 estimate for a singular entangled quadrilinear form, Math. Res. Lett. 22 (2015), no. 5, 1317-1332. 1412.2384.