Pavel Zorin-Kranich

activity

20102024

most citedVariation estimates for averages along primes and polynomials

40 citations · 489 across the 52 of their papers we have counts for

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26 papers · 1 filter

math.CA2023

$L^{p}$ integrability of functions with Fourier support on a smooth space curve

Shaoming Guo, Alex Iosevich, Ruixiang Zhang +1

We prove that if $f \in L^{p} (R^{k})$ with $p < (k^{2} + k + 2) /2$ satisfies that $f$ is supported on a small perturbation of the moment curve in $R^{k}$ , then $f$ is…

math.CA2021★ 1 cited

A stationary set method for estimating oscillatory integrals

Saugata Basu, Shaoming Guo, Ruixiang Zhang +1

We propose a new method of estimating oscillatory integrals, which we call a stationary set method. We use it to obtain the sharp convergence exponents of Tarry's problems in dimen…

math.CA2020★ 5 cited

Decoupling inequalities for quadratic forms

Shaoming Guo, Changkeun Oh, Ruixiang Zhang +1

We prove sharp $ℓ^{q} L^{p}$ decoupling inequalities for $p, q \in [2, \infty)$ and arbitrary tuples of quadratic forms. Connections to prior results on decoupling inequalities for qu…

math.CA2020

A variable coefficient multi-frequency lemma

Shaoming Guo, Pavel Zorin-Kranich

We show a variable coefficient version of Bourgain's multi-frequency lemma. It can be used to obtain major arc estimates for a discrete Stein--Wainger type operator considered by K…

math.CA2020★ 2 cited

Variational truncations of singular integrals on spaces of homogeneous type

Pavel Zorin-Kranich

We prove sharp weighted estimates for $r$ -variations of averages and truncated singular integrals on suitable spaces of homogeneous type, including homogeneous nilpotent Lie groups…

math.CA2019★ 6 cited

Decoupling for two quadratic forms in three variables: a complete characterization

Shaoming Guo, Changkeun Oh, Joris Roos +2

We prove sharp decoupling inequalities for all degenerate surfaces of codimension two in $R^{5}$ given by two quadratic forms in three variables. Together with previous work…

math.CA2019★ 1 cited

Modulation invariant operators

Pavel Zorin-Kranich

The first three results in this thesis are motivated by a far-reaching conjecture on boundedness of singular Brascamp-Lieb forms. Firstly, we improve over the trivial estimate for…

math.CA2019★ 7 cited

Decoupling for certain quadratic surfaces of low co-dimensions

Shaoming Guo, Pavel Zorin-Kranich

We prove sharp $ℓ^{p} L^{p}$ decoupling inequalities for $2$ quadratic forms in $4$ variables. We also recover several previous results (arXiv:1409.1634, arXiv:1501.07224, arXiv:…

math.CA2018★ 29 cited

Jump inequalities for translation-invariant operators of Radon type on $Z^{d}$

Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich

We prove strong jump inequalities for a large class of operators of Radon type in the discrete and ergodic theoretical settings. These inequalities are the $r = 2$ endpoints of the $…

math.CA2018★ 29 cited

A bootstrapping approach to jump inequalities and their applications

Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich

The aim of this paper is to present an abstract and general approach to jump inequalities in harmonic analysis. Our principal conclusion is the refinement of $r$ -variational estima…

math.CA2018★ 26 cited

Jump inequalities via real interpolation

Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich

Jump inequalities are the $r = 2$ endpoint of Lépingle's inequality for $r$ -variation of martingales. Extending earlier work by Pisier and Xu we interpret these inequalities in terms…

math.CA2018★ 9 cited

Kakeya-Brascamp-Lieb inequalities

Pavel Zorin-Kranich

We prove a sharp common generalization of endpoint multilinear Kakeya and local discrete Brascamp-Lieb inequalities.

math.CA2018★ 7 cited

Band-limited maximizers for a Fourier extension inequality on the circle

Diogo Oliveira e Silva, Christoph Thiele, Pavel Zorin-Kranich

Among the class of functions with Fourier modes up to degree 30, constant functions are the unique real-valued maximizers for the endpoint Tomas-Stein inequality on the circle.

math.CA2017★ 24 cited

Maximal polynomial modulations of singular integrals

Pavel Zorin-Kranich

Let $K$ be a standard Hölder continuous Calderón--Zygmund kernel on $R^{d}$ whose truncations define $L^{2}$ bounded operators. We show that the maximal operator ob…

math.CA2017

A Uniform Random Pointwise Ergodic Theorem

Ben Krause, Pavel Zorin-Kranich

Let $a_{n}$ be the random increasing sequence of natural numbers which takes each value independently with decreasing probability of order $n^{- α}$ , $0 < α < 1/2$ . We prove that, almo…

math.CA2017★ 22 cited

Square functions for bi-Lipschitz maps and directional operators

Francesco Di Plinio, Shaoming Guo, Christoph Thiele +1

First we prove a Littlewood-Paley diagonalization result for bi-Lipschitz perturbations of the identity map on the real line. This result entails a number of corollaries for the Hi…

math.CA2016★ 10 cited

$A_{p}$ - $A_{\infty}$ estimates for multilinear maximal and sparse operators

Pavel Zorin-Kranich

We obtain mixed $A_{p}$ -- $A_{\infty}$ estimates for a large family of multilinear maximal and sparse operators. Operators from this family are known to control for instance multilinear…

math.CA2016★ 21 cited

Sparse domination on non-homogeneous spaces with an application to $A_{p}$ weights

Alexander Volberg, Pavel Zorin-Kranich

We extend Lerner's recent approach to sparse domination of Calderón--Zygmund operators to upper doubling (but not necessarily doubling), geometrically doubling metric measure space…

math.CA2016★ 3 cited

Intrinsic square functions with arbitrary aperture

Pavel Zorin-Kranich

We consider intrinsic square functions defined using (log-)Dini continuous test functions on spaces of homogeneous type. We prove weighted estimates with optimal (at least in the E…

math.CA2016★ 14 cited

Sparse domination of sharp variational truncations

Fernanda Clara de França Silva, Pavel Zorin-Kranich

We provide a versatile formulation of Lacey's recent sparse pointwise domination technique with a local weak type estimate on a nontangential maximal function as the only hypothesi…

math.CA2015★ 13 cited

Cancellation for the simplex Hilbert transform

Pavel Zorin-Kranich

We show that the truncated simplex Hilbert transform enjoys some cancellation in the sense that its norm grows sublinearly in the number of scales retained in the truncation. This…

math.CA2015★ 17 cited

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 $L^{p}$ …

math.CA2014★ 22 cited

Variational estimates for averages and truncated singular integrals along the prime numbers

Mariusz Mirek, Bartosz Trojan, Pavel Zorin-Kranich

We prove, in a unified way, $r$ -variational estimates, $r > 2$ , on $ℓ^{s} (Z)$ spaces, $s \in (1, \infty)$ , for averages and truncated singular integrals along the set of…

math.CA2014★ 28 cited

Weighted and vector-valued variational estimates for ergodic averages

Ben Krause, Pavel Zorin-Kranich

We prove weighted and vector-valued variational estimates for ergodic averages on $R^{d}$ . The weighted square function estimate relating ergodic averages to the dyadic mart…

Lp integrability of functions with Fourier support on a smooth space curve

A stationary set method for estimating oscillatory integrals

Decoupling inequalities for quadratic forms

A variable coefficient multi-frequency lemma

Variational truncations of singular integrals on spaces of homogeneous type

Decoupling for two quadratic forms in three variables: a complete characterization

Modulation invariant operators

Decoupling for certain quadratic surfaces of low co-dimensions

Jump inequalities for translation-invariant operators of Radon type on Zd

A bootstrapping approach to jump inequalities and their applications

Jump inequalities via real interpolation

Kakeya-Brascamp-Lieb inequalities

Band-limited maximizers for a Fourier extension inequality on the circle

Maximal polynomial modulations of singular integrals

A Uniform Random Pointwise Ergodic Theorem

Square functions for bi-Lipschitz maps and directional operators

Ap​-A∞​ estimates for multilinear maximal and sparse operators

Sparse domination on non-homogeneous spaces with an application to Ap​ weights

Intrinsic square functions with arbitrary aperture

Sparse domination of sharp variational truncations

Cancellation for the simplex Hilbert transform

Dyadic triangular Hilbert transform of two general and one not too general function

Variational estimates for averages and truncated singular integrals along the prime numbers

Weighted and vector-valued variational estimates for ergodic averages

$L^{p}$ integrability of functions with Fourier support on a smooth space curve

Jump inequalities for translation-invariant operators of Radon type on $Z^{d}$

$A_{p}$ - $A_{\infty}$ estimates for multilinear maximal and sparse operators

Sparse domination on non-homogeneous spaces with an application to $A_{p}$ weights