12 citations · 51 across the 25 of their papers we have counts for
28 papers
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…
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…
Dimensional estimates for measures on quaternionic spheres
Rami Ayoush, Michał Wojciechowski
In this article we provide lower bounds for the lower Hausdorff dimension of finite measures assuming certain restrictions on their quaternionic spherical harmonics expansion. This…
On Bernstein type quantitative estimates for Ornstein non-inequalities
Krystian Kazaniecki, Michał Wojciechowski
For the sequence of multi-indexes and we study the inequality \[ \|D^β f\|_{L_1(\mathbb{T}^d)}\leq K_N \sum_{j= 1}^{m} \|D^{α_j}f\|_{L_1(\mathbb{T}^d)}, \]…
The $H^1(\T^d)$-multiplier norm of Rajchman measures, Zafran-type phenomena, and Walsh--Stieltjes series
Przemysław Ohrysko, Michał Wojciechowski, Bartłomiej Zawalski
We study convolution by complex Rajchman measures as Fourier multipliers on the mean-zero part of the classical isotropic Hardy space $H^1(\T^d)$. Our main technical result gives a…
On the Embedding of Space into Besov-Orlicz Space
Aleksander Pawlewicz, Michał Wojciechowski
We give a sufficient (and, in the case of a compact domain, a necessary) condition for the embedding of Sobolev space of functions with integrable gradient into Besov-Orlicz spaces…
Marcinkiewicz Sampling Theorem for Orlicz Spaces
Aleksander Pawlewicz, Michał Wojciechowski
In the article we generalize the Marcinkiewicz sampling theorem in the context of Orlicz spaces. We establish conditions under which sampling theorem holds in terms of restricted s…
Microlocal approach to the Hausdorff dimension of measures
Rami Ayoush, Michał Wojciechowski
In this paper we study the dependence of geometric properties of Radon measures, such as Hausdorff dimension and rectifiability of singular sets, on the wavefront set. This is achi…
Hausdorff dimension of measures with arithmetically restricted spectrum
Rami Ayoush, Dmitriy Stolyarov, Michał Wojciechowski
We provide an estimate from below for the lower Hausdorff dimension of measures on the unit circle based on the arithmetic properties of their spectra. We obtain our bounds via app…
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.
Hoeffding decomposition in spaces
Maciej Rzeszut, Michał Wojciechowski
The well known result of Bourgain and Kwapień states that the projection onto the subspace of the Hilbert space spanned by functions depende…
Spectrally reasonable measures II
Przemysław Ohrysko, Michał Wojciechowski
A measure on a locally compact Abelian group is said to have a natural spectrum if its spectrum is equal to the closure of the range of the Fourier-Stieltjes transform. In this pap…
Martingale approach to Sobolev embedding theorems
Rami Ayoush, Dmitriy Stolyarov, Michal Wojciechowski
We prove a martingale analog of van Schaftingen's theorem and give sharp estimates on the lower Hausdorff dimension of measures in martingale shift invariant spaces. We also provid…
On dimension and regularity of bundle measures
Rami Ayoush, Michał Wojciechowski
In this paper we quantify the notion of antisymmetry of the Fourier transform of certain vector valued measures. The introduced scale is related to the condition appearing in Uchiy…
On the Pelczynski conjecture on Auerbach Bases
Andrzej Weber, Michał Wojciechowski
We consider Auerbach bases in Banach spaces of dimension n>2. We show that there exists at least (n-1)n/2+1 such bases. This estimate follows from the calculation of the Lusternik-…
Non-separability of the Gelfand space of measure algebras
P. Ohrysko, M. Wojciechowski, Colin C. Graham
We prove that there exists uncountably many pairwise disjoint open subsets of the Gelfand space of the measure algebra on any locally compact non-discrete abelian group which shows…
Spectrally reasonable measures
Przemysław Ohrysko, Michał Wojciechowski
In this paper we investigate the problems related to measures with a natural spectrum (equal to the closure of the set of the values of the Fourier-Stieltjes transform). Since it i…
Anisotropic Ornstein non inequalities
Krystian Kazaniecki, Dmitriy M. Stolyarov, Michal Wojciechowski
We investigate existence of a priori estimates for differential operators in norm: for anisotropic homogeneous differential operators , we study the c…
Independent sums of and
Maciej Rzeszut, Michal Wojciechowski
We construct a new idempotent Fourier multiplier on the Hardy space on the bidisc, which could not be obtained by applying known one dimentional results. The main tool is a new $L^…
On the equivalence between the sets of the trigonometric polynomials
Krystian Kazaniecki, Michał Wojciechowski
In this paper we construct an injection from the linear space of trigonometric polynomials defined on with bounded degrees with respect to each variable to a suitabl…
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 Gelfand space of the measure algebra on the circle group
Przemysław Ohrysko, Michał Wojciechowski
This paper is devoted to studying certain topological properties of the maximal ideal space of the measure algebra on the circle group. In particular, we focus on Cech cohomologies…
Dimension of gradient measures
Dmitriy M. Stolyarov, Michal Wojciechowski
We prove that if pure derivatives with respect to all coordinates of a function on are signed measures, then their lower Hausdorff dimension is at least . The d…