50 citations · 289 across the 33 of their papers we have counts for
19 papers · 1 filter
Large dilates of hypercube graphs in the plane
Vjekoslav Kovač, Bruno Predojević
We study a distance graph that is isomorphic to the -skeleton of an -dimensional unit hypercube. We show that every measurable set of positive upper Banach density in t…
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_…
Multi-parameter maximal Fourier restriction
Aleksandar Bulj, Vjekoslav Kovač
The main result of this note is the strengthening of a quite arbitrary a priori Fourier restriction estimate to a multi-parameter maximal estimate of the same type. This allows us…
On binomial sums, additive energies, and lazy random walks
Vjekoslav Kovač
We establish a sharp estimate for -additive energies of subsets of the discrete hypercube conjectured by de Dios Pont, Greenfeld, Ivanisvili, and Madrid in arXiv:2112.09352, whi…
Sharp estimates of powers of the complex Riesz transform
Andrea Carbonaro, Oliver Dragičević, Vjekoslav Kovač
Let be scalar Riesz transforms on . We prove that the norms of -th powers of the operator behave exactly as , uniformly in…
Density theorems for anisotropic point configurations
Vjekoslav Kovač
Several results in the existing literature establish Euclidean density theorems of the following strong type. These results claim that every set of positive upper Banach density in…
The density of sets containing large similar copies of finite sets
Kenneth Falconer, Vjekoslav Kovač, Alexia Yavicoli
We prove that if () is a Lebesgue-measurable set with density larger than , then contains similar copies of every -point…
A Szemerédi-type theorem for subsets of the unit cube
Polona Durcik, Vjekoslav Kovač
We investigate gaps of -term arithmetic progressions inside a positive measure subset of the unit cube . If lengths of their gaps are…
Fourier restriction implies maximal and variational Fourier restriction
Vjekoslav Kovač
We give an abstract argument that an a priori Fourier restriction estimate for a certain choice of exponents automatically implies maximal and variational Fourier restriction estim…
A variational restriction theorem
Vjekoslav Kovač, Diogo Oliveira e Silva
We establish variational estimates related to the problem of restricting the Fourier transform of a three-dimensional function to the two-dimensional Euclidean sphere. At the same…
A sharp nonlinear Hausdorff-Young inequality for small potentials
Vjekoslav Kovač, Diogo Oliveira e Silva, Jelena Rupčić
The nonlinear Hausdorff-Young inequality follows from the work of Christ and Kiselev. Later Muscalu, Tao, and Thiele asked if the constants can be chosen independently of the expon…
Power-type cancellation for the simplex Hilbert transform
Polona Durcik, Vjekoslav Kovač, Christoph Thiele
We prove bounds for the truncated simplex Hilbert transform which grow with a power less than one of the truncation range in the logarithmic scale.
On a trilinear singular integral form with determinantal kernel
Philip Gressman, Danqing He, Vjekoslav Kovač +3
We study a trilinear singular integral form acting on two-dimensional functions and possessing invariances under arbitrary matrix dilations and linear modulations. One part of the…
Dyadic triangular Hilbert transform of two general and one not too general function
Vjekoslav Kovač, Christoph Thiele, Pavel Zorin-Kranich
The so-called triangular Hilbert transform is an elegant trilinear singular integral form which specializes to many well studied objects of harmonic analysis. We investigate …
Sobolev norm estimates for a class of bilinear multipliers
Frédéric Bernicot, Vjekoslav Kovač
We consider bilinear multipliers that appeared as a distinguished particular case in the classification of two-dimensional bilinear Hilbert transforms by Demeter and Thiele [9]. In…
A T(1) theorem for entangled multilinear dyadic Calderón-Zygmund operators
Vjekoslav Kovač, Christoph Thiele
We prove a boundedness criterion for a class of dyadic multilinear forms acting on two-dimensional functions. Their structure is more general than the one of classical multilinear…
Bellman function technique for multilinear estimates and an application to generalized paraproducts
Vjekoslav Kovač
We prove L^p estimates for a class of two-dimensional multilinear forms that naturally generalize (dyadic variants of) both classical paraproducts and the twisted paraproduct intro…
Uniform constants in Hausdorff-Young inequalities for the Cantor group model of the scattering transform
Vjekoslav Kovač
Analogues of Hausdorff-Young inequalities for the Dirac scattering transform (a.k.a. SU(1,1) nonlinear Fourier transform) were first established by Christ and Kiselev [1],[2]. Late…
Boundedness of the twisted paraproduct
Vjekoslav Kovač
We prove L^p estimates for a two-dimensional bilinear operator of paraproduct type. This result answers a question posed by Demeter and Thiele in [3].