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math.FA2023
Alberti's type rank one theorem for martingales
Rami Ayoush, Dmitriy Stolyarov, Michał Wojciechowski
We prove that the polar decomposition of the singular part of a vector measure depends on its conditional expectations computed with respect to the -regular filtration. This dep…
math.FA2023
Schur property for jump parts of gradient measures
Krystian Kazaniecki, Anton Tselishchev, Michał Wojciechowski
We consider weakly null sequences in the Banach space of functions of bounded variation . We prove that for any such sequence the jump parts of…
math.FA2023
On the analytic version of the Mitiagin-DeLeeuw-Mirkhil non-inequality on bi-disc
Krystian Kazaniecki, Michał Wojciechowski
Using the method of Rudin-Shapiro polynomials we prove the analytic version of the Mitiagin-DeLeeuw-Mirkhil non-inequality for complex partial differential operators with constant…