2 citations · 4 across the 13 of their papers we have counts for
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The shifted bilinear Hilbert transform
Lars Becker, Polona Durcik
We prove estimates for the shifted bilinear Hilbert transform, with a polylogarithmic bound in the size of the shift. As applications, we obtain -variation estimates for b…
Sharp isoperimetric inequalities on the Hamming cube II: The critical exponent
Polona Durcik, Paata Ivanisvili, Joris Roos +1
A sharp isoperimetric inequality for the Hamming cube is proved at the critical exponent . This follows up on previous work, where such bounds were established for n…
On trilinear singular Brascamp-Lieb integrals
Lars Becker, Polona Durcik, Fred Yu-Hsiang Lin
We classify all trilinear singular Brascamp-Lieb forms, completing the classification in the two dimensional case by Demeter and Thiele in arXiv:0803.1268. We use known results in…
Sharp isoperimetric inequalities on the Hamming cube near the critical exponent
Polona Durcik, Paata Ivanisvili, Joris Roos
An isoperimetric inequality on the Hamming cube for exponents is proved, achieving equality on any subcube. This was previously known for $β\ge \log_2(3/2)\approx 0.…
Norm-variation of triple ergodic averages for commuting transformations
Polona Durcik, Lenka Slavíková, Christoph Thiele
We prove an -variation estimate, , in the norm for ergodic averages with respect to three commuting transformations. It is not known whether such estimates hold for all $r\…
A strong-type Furstenberg-Sárközy theorem for sets of positive measure
Polona Durcik, Vjekoslav Kovač, Mario Stipčić
For every , we prove that a positive measure subset of the unit square contains a point such that nontrivially intersects curves $y-y_…