arXiv subjects

Vjekoslav Kovač

Publications and source records attributed to Vjekoslav Kovač.

59 records · Page 4Linked to original sources

arXiv2013

A T(1) theorem for entangled multilinear dyadic Calderón-Zygmund operators

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 Calderón-Zygmund operators as several functions can now depend on the same one-dimensional variable. The study of this class is motivated by examples related to the two-dimensional bilinear Hilbert transform and to bilinear ergodic averages. This paper is a sequel to the prior paper arXiv:1108.0917 by the first author.

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arXiv2012

On a trilinear form related to the Carleson theorem

The main purpose of this short note is to present an adaptation of the multilinear Bellman function technique from [4] to the time-frequency analysis. Demeter and Thiele introduced the two-dimensional bilinear Hilbert transform in [3] and showed that the Carleson operator can be identified in particular instances of the corresponding trilinear form. Demeter considered the Walsh model of one such form in [2], in relation to the discussion of the Walsh-Carleson theorem. We prove boundedness of this trilinear form for a single triple of exponents at the boundary of the previously established range.

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arXiv2011

Bellman function technique for multilinear estimates and an application to generalized paraproducts

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 introduced in [5] and studied in [1] and [6]. The method we use builds on the approach from [6] and we present it as a rather general technique for proving estimates on dyadic multilinear operators. In the particular application to "generalized paraproducts" this method is combined with combinatorics of integer partitions.

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arXiv2010

Uniform constants in Hausdorff-Young inequalities for the Cantor group model of the scattering transform

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]. Later Muscalu, Tao, and Thiele [5] raised a question if the constants can be chosen uniformly in $1\leq p\leq 2$. Here we give a positive answer to that question when the Euclidean real line is replaced by its Cantor group model.

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arXiv2010

Boundedness of the twisted paraproduct

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].

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