3 citations · 4 across the 6 of their papers we have counts for
8 papers
On a Conjecture on Sharygin Triangles
Nikolay Osipov
By a simple method we prove the following conjecture on Sharygin triangles: there is only one Sharygin triangle (up to an isometry) whose vertices are chosen from the set of vertic…
Bellman function method for general operators on martingales: arbitrary regular filtrations
Nikolay N. Osipov
It has been recently shown that the Bellman function method can be applied in the general context of Gundy's extrapolation theorem for vector-valued martingales. But the additional…
From prediction markets to interpretable collective intelligence
Alexey V. Osipov, Nikolay N. Osipov
We outline how to create a mechanism that provides an optimal way to elicit, from an arbitrary group of experts, the probability of the truth of an arbitrary logical proposition to…
Bellman function method for general operators on martingales
Viacheslav Borovitskiy, Nikolay N. Osipov, Anton Tselishchev
It is shown that the Bellman function method can be applied to study the -norms of general operators on martingales, i.e., of operators that are not necessarily martingale tra…
Two types of Rubio de Francia operators on Triebel--Lizorkin and Besov spaces
Eugenia Malinnikova, Nikolay N. Osipov
We discuss generalizations of Rubio de Francia's inequality for Triebel--Lizorkin and Besov spaces, continuing the research from [5]. Two versions of Rubio de Francia's operator ar…
Sharp estimates of integral functionals on classes of functions with small mean oscillation
Paata Ivanisvili, Nikolay N. Osipov, Dmitriy M. Stolyarov +2
We unify several Bellman function problems into one setting. For that purpose we define a class of functions that have, in a sense, small mean oscillation (this class depends on tw…
Littlewood--Paley--Rubio de Francia inequality for the Walsh system
Nikolay N. Osipov
Rubio de Francia proved the one-sided Littlewood--Paley inequality for arbitrary intervals in , . In this article, such an inequality is proved for the Walsh…
Bellman function for extremal problems in BMO
Paata Ivanisvili, Nikolay Osipov, Dmitriy Stolyarov +2
In this paper we develop the method of finding sharp estimates by using a Bellman function. In such a form the method appears in the proofs of the classical John--Nirenberg inequal…