40 citations · 489 across the 52 of their papers we have counts for
7 papers · 1 filter
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.