Averages of simplex Hilbert transforms

Durcik, Polona; Roos, Joris

doi:10.1090/proc/15196

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Introduction1

Multilinear Anisotropic Singular Integrals1

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2020

2022

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Cited by 5 publications

(2 citation statements)

References 18 publications

(27 reference statements)

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“…The examples used to prove Theorem 1.5 are similar to the ones in [12] and [8]. Theorem 1.5 also implies that similarly the lower bound 2 m−1 in Theorem 1.2 can not be lowered.…”

Section: Introductionmentioning

confidence: 81%

Singular Brascamp–Lieb inequalities with cubical structure

Durcik

Thiele

2020

Bull. London Math. Soc.

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“…The examples used to prove Theorem 1.5 are similar to the ones in [12] and [8]. Theorem 1.5 also implies that similarly the lower bound 2 m−1 in Theorem 1.2 can not be lowered.…”

Section: Introductionmentioning

confidence: 81%

Singular Brascamp–Lieb inequalities with cubical structure

Durcik

Thiele

2020

Bull. London Math. Soc.

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“…Dyadic models of these problems are significantly easier: they have already been handled quite generally by the present author [40] and Stipčić [55], respectively. Otherwise, the only cases and variants of entangled singular integral forms studied so far are the so-called "twisted paraproduct operator" [20,41], the operators with cubical structure [12,13,21], and the operators that resemble multilinear Hilbert transforms [16,19,58,60].…”

Section: Multilinear Anisotropic Singular Integralsmentioning

confidence: 99%

Density theorems for anisotropic point configurations

Kovač

2021

Can. J. Math.-J. Can. Math.

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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 Euclidean space of an appropriate dimension contains isometric copies of all sufficiently large elements of a prescribed family of finite point configurations. So far, all results of this type discussed linear isotropic dilates of a fixed point configuration. In this paper, we initiate the study of analogous density theorems for families of point configurations generated by anisotropic dilations, i.e., families with power-type dependence on a single parameter interpreted as their size. More specifically, we prove nonisotropic power-type generalizations of a result by Bourgain on vertices of a simplex, a result by Lyall and Magyar on vertices of a rectangular box, and a result on distance trees, which is a particular case of the treatise of distance graphs by Lyall and Magyar. Another source of motivation for this paper is providing additional evidence for the versatility of the approach stemming from the work of Cook, Magyar, and Pramanik and its modification used recently by Durcik and the present author. Finally, yet another purpose of this paper is to single out anisotropic multilinear singular integral operators associated with the above combinatorial problems, as they are interesting on their own.

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Singular Brascamp–Lieb: A Survey

Durcik

Thiele

2021

Springer INdAM Series

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Averages of simplex Hilbert transforms

Cited by 5 publications

References 18 publications

Singular Brascamp–Lieb inequalities with cubical structure

Singular Brascamp–Lieb inequalities with cubical structure

Density theorems for anisotropic point configurations

Singular Brascamp–Lieb: A Survey

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