Zobrazeno 1 - 10
of 233
pro vyhledávání: '"Mastyło, Mieczysław"'
We investigate projection constants within classes of multivariate polynomials over finite-dimensional real Hilbert spaces. Specifically, we consider the projection constant for spaces of spherical harmonics and spaces of homogeneous polynomials as w
Externí odkaz:
http://arxiv.org/abs/2405.12123
Autor:
Mastyło, Mieczysław, Sinnamon, Gord
A Christ-Kiselev maximal theorem is proved for linear operators between quasi-Banach function lattices satisfying certain lattice geometrical conditions. The result is further explored for weighted Lorentz spaces, classical Lorentz spaces, and Wiener
Externí odkaz:
http://arxiv.org/abs/2401.00119
Autor:
Mastyło, Mieczysław, Sinnamon, Gord
Publikováno v:
Proceedings of the American Mathematical Society, 152(2024), 1099-1107
It is shown that if the Fourier transform is a bounded map on a rearrangement-invariant space of functions on $\mathbb R^n$, modified by a weight, then the weight is bounded above and below and the space is equivalent to $L^2$. Also, if it is bounded
Externí odkaz:
http://arxiv.org/abs/2302.07047
Asymptotic insights for projection, Gordon-Lewis and Sidon constants in Boolean cube function spaces
The main aim of this work is to study important local Banach space constants for Boolean cube function spaces. Specifically, we focus on $\mathcal{B}_{\mathcal{S}}^N$, the finite-dimensional Banach space of all real-valued functions defined on the $N
Externí odkaz:
http://arxiv.org/abs/2302.00233
Given a frequency sequence $\omega=(\omega_n)$ and a finite subset $J \subset \mathbb{N}$, we study the space $\mathcal{H}_{\infty}^{J}(\omega)$ of all Dirichlet polynomials $D(s) := \sum_{n \in J} a_n e^{-\omega_n s}, \, s \in \mathbb{C}$. The main
Externí odkaz:
http://arxiv.org/abs/2302.00231
We study the projection constant of the space of operators on $n$-dimensional Hilbert spaces, with the trace norm, $\mathcal S_1(n)$. We show an integral formula for the projection constant of $\mathcal S_1(n)$; namely $ \boldsymbol{\lambda}\big(\mat
Externí odkaz:
http://arxiv.org/abs/2302.00218
The general problem we address is to develop new methods in the study of projection constants of Banach spaces of multivariate polynomials. The relative projection constant $\boldsymbol{\lambda}(X,Y)$ of a subspace $X$ of a Banach $Y$ is the smallest
Externí odkaz:
http://arxiv.org/abs/2208.06467
We prove stronger variants of a multiplier theorem of Kislyakov. The key ingredients are based on ideas of Kislaykov and the Kahane-Salem-Zygmund inequality. As a by-product we show various multiplier theorems for spaces of trigonometric polynomials
Externí odkaz:
http://arxiv.org/abs/2107.10131
Given a bounded measurable function $\sigma$ on $\mathbb{R}^n$, we let $T_\sigma $ be the operator obtained by multiplication on the Fourier transform by $\sigma $. Let $0
Externí odkaz:
http://arxiv.org/abs/2008.11490
Autor:
Defant, Andreas, Mastyło, Mieczysław
The main aim of this work is to give a general approach to the celebrated Kahane-Salem-Zygmund inequalities. We prove estimates for exponential Orlicz norms of averages $\sup_{1\le j \leq N} \big |\sum_{1 \leq i \leq K}\gamma_i(\cdot) a_{i,j}\big|$ w
Externí odkaz:
http://arxiv.org/abs/2008.04429