40 citations · 489 across the 52 of their papers we have counts for
52 papers
Lipschitz estimates in the Besov settings for Young and rough differential equations
Peter Friz, Hannes Kern, Pavel Zorin-Kranich
We develop a set of techniques that enable us to effectively recover Besov rough analysis from p-variation rough analysis. Central to our approach are new metric groups, in which s…
integrability of functions with Fourier support on a smooth space curve
Shaoming Guo, Alex Iosevich, Ruixiang Zhang +1
We prove that if with satisfies that is supported on a small perturbation of the moment curve in , then is…
Fefferman-Stein inequality for maximal functions of martingales in uniformly smooth spaces
Pavel Zorin-Kranich
Let be a martingale with values in a uniformly -smooth Banach space and any positive weight. We show that …
Weighted Davis inequalities for martingale square functions
Dennis Wollgast, Pavel Zorin-Kranich
For a Hilbert space valued martingale and an adapted sequence of positive random variables , we show the weighted Davis type inequality \[ \mathbb{E} \Bigl( |f_0| w_…
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…
Improved surrogate bi-parameter maximum principle
Pavel Mozolyako, Georgios Psaromiligkos, Alexander Volberg +1
Logarithmic potentials and many other potentials satisfy maximum principle. The dyadic version of logarithmic potential can be easily introduced, it lives on dyadic tree and also s…
Decoupling inequalities for quadratic forms
Shaoming Guo, Changkeun Oh, Ruixiang Zhang +1
We prove sharp decoupling inequalities for and arbitrary tuples of quadratic forms. Connections to prior results on decoupling inequalities for qu…
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…
Variational truncations of singular integrals on spaces of homogeneous type
Pavel Zorin-Kranich
We prove sharp weighted estimates for -variations of averages and truncated singular integrals on suitable spaces of homogeneous type, including homogeneous nilpotent Lie groups…
Rough semimartingales and -variation estimates for martingale transforms
Peter Friz, Pavel Zorin-Kranich
We establish a new scale of -variation estimates for martingale paraproducts, martingale transforms, and Itô integrals, of relevance in rough paths theory, stochastic, and harmo…
Carleson embedding on tri-tree and on tri-disc
Pavel Mozolyako, Georgios Psaromiligkos, Alexander Volberg +1
We prove multi-parameter dyadic embedding theorem for Hardy operator on the multi-tree. We also show that for a large class of Dirichlet spaces in bi-disc and tri-disc this proves…
A short proof of decoupling for the moment curve
Shaoming Guo, Zane Kun Li, Po-Lam Yung +1
We give a short and elementary proof of the decoupling inequality for the moment curve in , using a bilinear approach inspired by the nested efficient cong…
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 given by two quadratic forms in three variables. Together with previous work…
Weighted Lépingle inequality
Pavel Zorin-Kranich
We prove an estimate for weighted -th moments of the pathwise -variation of a martingale in terms of the characteristic of the weight. The novelty of the proof is tha…
Bi-parameter Carleson embeddings with product weights
Nicola Arcozzi, Pavel Mozolyako, Georgios Psaromiligkos +2
Coifman--Meyer multipliers represent a very important class of bi-linear singular operators, which were extensively studied and generalized. They have a natural multi-parameter cou…
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…
Decoupling for certain quadratic surfaces of low co-dimensions
Shaoming Guo, Pavel Zorin-Kranich
We prove sharp decoupling inequalities for quadratic forms in variables. We also recover several previous results (arXiv:1409.1634, arXiv:1501.07224, arXiv:…
Variational estimates for martingale paraproducts
Vjekoslav Kovač, Pavel Zorin-Kranich
We show that bilinear variational estimates of Do, Muscalu, and Thiele (arXiv:1009.5187) remain valid for a pair of general martingales with respect to the same filtration. Our res…
Decoupling for moment manifolds associated to Arkhipov--Chubarikov--Karatsuba systems
Shaoming Guo, Pavel Zorin-Kranich
We prove decoupling inequalities for a class of moment manifolds. These inequalities imply optimal mean value estimates for multidimensional Weyl sums of the kind c…
Jump inequalities for translation-invariant operators of Radon type on
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 endpoints of the $…
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 -variational estima…
Jump inequalities via real interpolation
Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich
Jump inequalities are the endpoint of Lépingle's inequality for -variation of martingales. Extending earlier work by Pisier and Xu we interpret these inequalities in terms…
Kakeya-Brascamp-Lieb inequalities
Pavel Zorin-Kranich
We prove a sharp common generalization of endpoint multilinear Kakeya and local discrete Brascamp-Lieb inequalities.
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.