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math.FA2024
On the relations between Auerbach or almost Auberbach Markushevich systems and Schauder bases
Beata Randrianantoanina, Michał Wojciechowski, Pavel Zatitskii
We establish that the summability of the series is the necessary and sufficient criterion ensuring that every Markushevich basis in a separa…
math.FA2023
Monotone rearrangement in averaging classes
Marat Abdrakhmanov, Leonid Slavin, Pavel Zatitskii
We consider a general collection of function classes on the interval defined in terms of certain averages and show that monotone rearrangement does not increase the class c…
math.FA2023
Monotone rearrangement does not increase generalized Campanato norm in VMO
Leonid Slavin, Pavel Zatitskii
We consider a quantitative version of the space VMO on an interval, equipped with a quadratic Campanato-type norm, and prove that monotone rearrangement does not increase the norm…