12 citations · 20 across the 10 of their papers we have counts for
8 papers · 1 filter
Diagonal operators on Janson-Sobolev and Janson-Sobolev-Hardy spaces
Krystian Kazaniecki, Richard Lechner
We study the Banach space and operator factorization structure of Janson-Sobolev and Janson-Sobolev-Hardy spaces. This new class of martingale spaces is determined by a -adic fi…
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…
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…
Martingale Type, the Gamlen-Gaudet Construction and a Greedy Algorithm
Krystian Kazaniecki, Paul F. X. Müller
In the present paper we identify those filtered probability spaces that determine already the martingale type of a…
On Bernstein type quantitative estimates for Ornstein non-inequalities
Krystian Kazaniecki, Michał Wojciechowski
For the sequence of multi-indexes and we study the inequality \[ \|D^β f\|_{L_1(\mathbb{T}^d)}\leq K_N \sum_{j= 1}^{m} \|D^{α_j}f\|_{L_1(\mathbb{T}^d)}, \]…
An invariant variant of the little Grothendieck theorem for Sobolev spaces
Krystian Kazaniecki, Piotr Pakosz, Michał Wojciechowski
We prove that every Hilbert space operator which factorizes invariantly through Sobolev space belongs to some non-trivial Schatten class.
Ornstein's non-inequalities Riesz product approach
Krystian Kazaniecki, Michał Wojciechowski
We provide a new technique to prove Ornstein's non-inequalities for derivatives with some geometrical dependence on their indexes.
On the continuity of Fourier multipliers on the homogeneous Sobolev spaces
Krystian Kazaniecki, Michał Wojciechowski
In this paper we proof that every Fourier multiplier on homogeneous sobolev space is a continuous function. Our theorem is generalization of A. Bonami a…