
Vjekoslav Kovač
Email address:
Postal address:
Department of Mathematics
Faculty of Science
University of Zagreb
Bijenička cesta 30
10000 Zagreb
CROATIA
Office: A310


Research publications and preprints:
[36] 
On binomial sums, additive energies, and lazy random walks,
preprint, submitted.
∫ An ancillary Mathematica notebook is available here. 
[arXiv] 
[35] 
Asymptotic behavior of $L^p$ estimates for a class of multipliers with homogeneous unimodular symbols
(with A. Bulj),
preprint, submitted. 
[arXiv] 
[34] 
Bilinear embedding in Orlicz spaces for divergenceform operators with complex coefficients
(with K. A. Škreb),
preprint, submitted. 
[arXiv] 
[33] 
Sharp $L^p$ estimates of powers of the complex Riesz transform
(with A. Carbonaro and O. Dragičević),
Math. Ann., published online (2022), 45 pp. 
[arXiv] [journal] 
[32] 
Asymptotically sharp discrete nonlinear HausdorffYoung inequalities for the SU(1,1)valued Fourier products
(with D. Oliveira e Silva and J. Rupčić),
Q. J. Math., published online (2022), 10 pp. 
[arXiv] [journal] 
[31] 
Popular differences for right isosceles triangles,
Electron. J. Combin. 28 (2021), no. 4, Article P4.27, 10 pp. 
[arXiv] [journal] 
[30] 
Trilinear embedding for divergenceform operators with complex coefficients
(with A. Carbonaro, O. Dragičević, and K. A. Škreb),
preprint, submitted. 
[arXiv] 
[29] 
Pointwise convergence of certain continuoustime double ergodic averages
(with M. Christ, P. Durcik, and J. Roos),
Ergodic Theory Dynam. Systems. 42 (2022), no. 7, 22702280. 
[arXiv] [journal] 
[28] 
The density of sets containing large similar copies of finite sets
(with K. Falconer and A. Yavicoli),
accepted for publication in J. Anal. Math. 
[arXiv] [journal] 
[27] 
Density theorems for anisotropic point configurations,
accepted for publication in Canad. J. Math. 
[arXiv] [journal] 
[26] 
Convergence of ergodicmartingale paraproducts
(with M. Stipčić),
Statist. Probab. Lett. 164 (2020), Article 108826, 6 pp. 
[arXiv] [journal] 
[25] 
A Szemeréditype theorem for subsets of the unit cube
(with P. Durcik),
Anal. PDE. 15 (2022), no. 2, 507549. 
[arXiv] [journal] 
[24] 
Improving estimates for discrete polynomial averages
(with R. Han, M. T. Lacey, J. Madrid, and F. Yang),
J. Fourier Anal. Appl. 26 (2020), Article 42, 11 pp. 
[arXiv] [journal] 
[23] 
Variational estimates for martingale paraproducts
(with P. ZorinKranich),
Electron. Commun. Probab. 24 (2019), paper no. 48, 14 pp. 
[arXiv] [journal] 
[22] 
Fourier restriction implies maximal and variational Fourier restriction,
J. Funct. Anal. 277 (2019), no. 10, 33553372.
∫ A nice discussion of the proof was written by M. Vitturi on
his blog. 
[arXiv] [journal] 
[21] 
A variational restriction theorem
(with D. Oliveira e Silva),
Arch. Math. 117 (2021), 6578. 
[arXiv] [journal] 
[20] 
Boxes, extended boxes, and sets of positive upper density in the Euclidean space
(with P. Durcik),
Math. Proc. Cambridge Philos. Soc. 171 (2021), no. 3, 481501. 
[arXiv] [journal] 
[19] 
Characterizations of democratic systems of translates on locally compact abelian groups
(with H. Šikić),
Monatsh. Math. 189 (2019), no. 3, 459485. 
[arXiv] [journal] 
[18] 
A sharp nonlinear HausdorffYoung inequality for small potentials
(with D. Oliveira e Silva and J. Rupčić),
Proc. Amer. Math. Soc. 147 (2019), no. 1, 239253.
∫ An ancillary Mathematica notebook is available here. 
[arXiv] [journal] 
[17] 
On side lengths of corners in positive density subsets of the Euclidean space
(with P. Durcik and L. Rimanić),
Int. Math. Res. Not. 2018, no. 22, 68446869. 
[arXiv] [journal] 
[16] 
Bellman functions and $L^p$ estimates for paraproducts
(with K. A. Škreb),
Probab. Math. Statist. 38 (2018), no. 2, 459479.
∫ An ancillary Mathematica notebook is available here. 
[arXiv] [journal] 
[15] 
Powertype cancellation for the simplex Hilbert transform
(with P. Durcik and C. Thiele),
J. Anal. Math. 139 (2019) 6782. 
[arXiv] [journal] 
[14] 
On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands
(with B. Gumhalter, F. Caruso, H. Lambert, and F. Giustino),
Phys. Rev. B. 94 (2016), no. 3, 035103, 16 pp + 4 pp suppl. 
[arXiv] [journal] 
[13] 
Norm variation of ergodic averages with respect to two commuting transformations
(with P. Durcik, K. A. Škreb, and C. Thiele),
Ergodic Theory Dynam. Systems 39 (2019), no. 3, 658688. 
[arXiv] [journal] 
[12] 
On a trilinear singular integral form with determinantal kernel
(with P. Gressman, D. He, B. Street, C. Thiele, and P.L. Yung),
Proc. Amer. Math. Soc. 144 (2016), no. 8, 34653477. 
[arXiv] [journal] 
[11] 
Dyadic triangular Hilbert transform of two general functions and one not too general function
(with C. Thiele and P. ZorinKranich),
Forum Math. Sigma 3 (2015), e25, 27pp. 
[arXiv] [journal] 
[10] 
Quantitative norm convergence of double ergodic averages associated with two commuting group actions,
Ergodic Theory Dynam. Systems 36 (2016), no. 3, 860874. 
[arXiv] [journal] 
[9] 
From electrostatic potentials to yet another triangle center
(with H. Abraham),
Forum Geom. 15 (2015), 7389. 
[arXiv] [journal] 
[8] 
On the share of closed IL formulas which are also in GL
(with V. Čačić),
Arch. Math. Logic. 54 (2015), no. 7, 741767. 
[arXiv] [journal] 
[7] 
Sobolev norm estimates for a class of bilinear multipliers
(with F. Bernicot),
Commun. Pure Appl. Anal. 13 (2014), no. 3, 13051315. 
[arXiv] [journal] 
[6] 
One modification of the martingale transform and its applications to paraproducts and stochastic integrals
(with K. A. Škreb),
J. Math. Anal. Appl. 426 (2015), no. 2, 11431163. 
[arXiv] [journal] 
[5] 
A T(1) theorem for entangled multilinear dyadic CalderónZygmund operators
(with C. Thiele),
Illinois J. Math. 57 (2013), no. 3, 775799. 
[arXiv] [journal] 
[4] 
On a trilinear form related to the Carleson theorem,
J. Math. Anal. Appl. 405 (2013), no. 1, 220226. 
[arXiv] [journal] 
[3] 
Bellman function technique for multilinear estimates and an application to generalized paraproducts,
Indiana Univ. Math. J. 60 (2011), no. 3, 813846. 
[arXiv] [journal] 
[2] 
Uniform constants in HausdorffYoung inequalities for the Cantor group model of the scattering transform,
Proc. Amer. Math. Soc. 140 (2012), no. 3, 915926. 
[arXiv] [journal] 
[1] 
Boundedness of the twisted paraproduct,
Rev. Mat. Iberoam. 28 (2012), no. 4, 11431164. 
[arXiv] [journal] 
Extended abstracts:
Talk slides:
 Density theorems for large copies of finite configurations (slides),
Short Communications Satellite of the International Congress of Mathematicians 2022 (SCS2022), July 2022.
 Lower bounds for the $L^p$ norms of some Fourier multipliers (seminar talk slides),
Probability and Analysis Webinar, May 2022.
Here is a video of the talk.
 Bilinear and trilinear estimates for semigroups generated by complex elliptic operators (seminar talk slides),
Virtual Harmonic Analysis Seminar, UK Harmonic Analysis group, February 2022.
 Density theorems for anisotropic point configurations (conference talk slides),
2021 Canadian Mathematical Society Winter Meeting, December 2021.
 Tales on two commuting transformations or flows (conference talk slides),
8th European Congress of Mathematics, Portorož, Slovenia, June 2021.
 Density theorems for Euclidean point configurations (conference talk slides), CroatianGerman meeting on analysis and mathematical physics, March 2021; similar talks were given at LMS Harmonic Analysis and PDEs Meeting in December 2020 and Analysis and PDE Webinar, IMPA, Rio de Janeiro in July 2020.
 Trilinear embedding for divergenceform operators (conference talk slides),
ApplMath20, Brijuni, September 2020.
 A Szemeréditype theorem for subsets of the unit cube (seminar talk slides),
Analysis Seminar, Georgia Institute of Technology, Atlanta, January 2020; University of Alabama analysis seminar, Tuscaloosa, February 2020; Mathematical Institute, University of Bonn (online seminar), July 2020.
 Improving estimates for discrete polynomial averaging operators (workshop talk slides),
Zagreb Workshop on Operator Theory 2020, Zagreb, June 2020.
 Variants of the ChristKiselev lemma and an application to the maximal Fourier restriction (seminar talk slides),
Seminar AlpeJadran, University of Zagreb, May 2019; Georgia Tech analysis seminar, Atlanta, September 2019.
 On maximal and variational Fourier restriction (workshop talk slides),
Followup workshop to trimester program Harmonic Analysis and Partial Differential Equations, Hausdorff Institute, Bonn, May 2019; Caltech/UCLA joint Analysis seminar, Pasadena, December 2019.
 A sharp nonlinear HausdorffYoung inequality for small potentials (workshop talk slides),
Real Analysis, Harmonic Analysis, and Applications, Oberwolfach, July 2017.
 Bellman functions and $L^p$ estimates for paraproducts (conference talk slides),
Harmonic analysis, complex analysis, spectral theory and all that, Będlewo, August 2016.
 Scattering theory analogues of several classical estimates in Fourier analysis (conference talk slides),
6th Croatian Mathematical Congress, Zagreb, June 2016.
 Normvariation of bilinear averages (conference talk slides),
Probabilistic Aspects of Harmonic Analysis, Będlewo, May 2016;
Singular integrals and partial differential equations, Helsinki, May 2016.
 Paraproducts with general dilations (conference talk slides),
AMS / EMS / SPM International Meeting, Porto, June 2015.
 Multilinear singular integrals with entangled structure (workshop talk slides),
Real Analysis, Harmonic Analysis and Applications, Oberwolfach, July 2014.
 Quantitative norm convergence of some ergodic averages (conference talk slides),
Probabilistic Aspects of Harmonic Analysis, Będlewo, April 2014.
 Estimates for a class of nonstandard bilinear multipliers (conference talk slides),
Joint CRMISAAC Conference on Fourier Analysis and Approximation Theory, Barcelona, November 2013.
 A T(1)type theorem for entangled multilinear CalderónZygmund operators (conference talk slides),
Joint International Meeting of the American Mathematical Society and the Romanian Mathematical Society, Alba Iulia, June 2013.
 On Twisted Paraproducts and some other Multilinear Singular Integrals (conference talk slides),
9th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, June 2012;
The 24th International Conference on Operator Theory, Timisoara, July 2012.
 Multilinear Twisted Paraproducts (seminar talk slides),
UCLA analysis seminar, Los Angeles, April 2012.
 Boundedness of the Twisted Paraproduct (seminar talk slides),
Indiana University, Bloomington, January 2011; University of Bonn, February 2011.
 Some Examples of Scaling Sets (conference talk slides),
3rd Croatian Mathematical Congress, Split, June 2004.
Talk slides in Croatian:
 Polugrupe generirane kompleksnim eliptičkim operatorima i ocjene u Orliczevim prostorima (in Croatian, seminar talk slides),
Seminar for functional analysis, University of Zagreb, January 2022.
 Problemi klasične i maksimalne teorije Fourierove restrikcije (in Croatian, seminar talk slides),
Seminar for differential equations and numerical analysis, University of Zagreb, April 2019.
 Neke primjene multilinearnih singularnih integrala (in Croatian, colloquium talk slides), University of Split, January 2019; similar talks were given in Zagreb (January 2012), Rijeka (February 2012), and Osijek (November 2015).
 Ekstremi potencijala i karakteristične točke trokuta (in Croatian, seminar talk slides),
Geometry seminar, University of Zagreb, March 2015.
Theses:
Supervision of doctoral students:
 M. Stipčić, Multilinear singular integrals associated with hypergraphs,
doctoral dissertation at the University of Zagreb, defended December 2020.
 J. Rupčić, Nonlinear SU(1,1)valued Fourier analysis,
doctoral dissertation at the University of Zagreb (in Croatian), defended June 2017.
 K. A. Škreb, The Bellman function technique for multilinear martingale estimates,
doctoral dissertation at the University of Zagreb (in Croatian), defended June 2017.
Editorial work:
 Managing editor of the research journal Glasnik Matematički.
The journal has a long tradition and it aims to keep its reputation. We welcome fine submissions in all fields of pure and applied math.
 Member of the editorial board of the professional electronic journal math.e, published in Croatian.
Lecture notes in English:
