Zobrazeno 1 - 10
of 369
pro vyhledávání: '"Tikhonov, Sergey"'
Autor:
Kolomoitsev, Yurii, Tikhonov, Sergey
We obtain Marcinkiewicz--ygmund (MZ) inequalities in various Banach and quasi-Banach spaces under minimal assumptions on the structural properties of these spaces. Our main results show that the Bernstein inequality in a general quasi-Banach function
Externí odkaz:
http://arxiv.org/abs/2411.04119
Autor:
Tikhonov, Sergey V.
We prove the finiteness of the genus of finite-dimensional division algebras over many infinitely generated fields. More precisely, let $K$ be a finite field extension of a field which is a purely transcendental extension of infinite transcendence de
Externí odkaz:
http://arxiv.org/abs/2409.19321
Autor:
Saucedo, Miquel, Tikhonov, Sergey
We prove that the Hausdorff--Young inequality $\|{\widehat{f}}\|_{q(\cdot)} \leq C \|{f}\|_{p(\cdot)}$ with $q(x)=p'(1/x)$ and $p(\cdot)$ even and non-decreasing holds in variable Lebesgue spaces if and only if $p$ is a constant. However, under the a
Externí odkaz:
http://arxiv.org/abs/2407.05503
Autor:
Kosov, Egor, Tikhonov, Sergey
We obtain new sampling discretization results in Orlicz norms on finite dimensional spaces. As applications, we study sampling recovery problems, where the error of the recovery process is calculated with respect to different Orlicz norms. In particu
Externí odkaz:
http://arxiv.org/abs/2406.03444
We extend the affine inequalities on $\mathbb{R}^n$ for Sobolev functions in $W^{s,p}$ with $1 \leq p < n/s$ obtained recently by Haddad-Ludwig [16, 17] to the remaining range $p \geq n/s$. For each value of $s$, our results are stronger than affine
Externí odkaz:
http://arxiv.org/abs/2405.07329
Autor:
Saucedo, Miquel, Tikhonov, Sergey
It is well known that if a function $f$ satisfies $$\|f(x) e^{\pi \alpha |x|^2}\|_p + \| \widehat{f}(\xi) e^{\pi \alpha |\xi|^2} \|_q<\infty \qquad\qquad\qquad(*)$$ with $\alpha=1$ and $1\le p,q<\infty$, then $f\equiv 0.$ We prove that if $f$ satisfi
Externí odkaz:
http://arxiv.org/abs/2404.07375
In this paper, we study the form of the constant $C$ in the Bernstein--Nikolskii inequalities $\|f^{(s)}\|_q \lesssim C(s, p, q)\left\|f\right\|_p,\,0
Externí odkaz:
http://arxiv.org/abs/2403.13149
Autor:
Goutor, Alina G., Tikhonov, Sergey V.
In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/2403.10999
We study norm inequalities for the Fourier transform, namely, \begin{equation}\label{introduction} \|\widehat f\|_{X_{p,q}^\lambda} \lesssim \|f\|_{Y}, \end{equation} where $X$ is either a Morrey or Campanato space and $Y$ is an appropriate function
Externí odkaz:
http://arxiv.org/abs/2309.12993
In this paper we obtain new quantitative estimates that improve the classical inequalities: Poincar\'e-Ponce, Gaussian Sobolev, and John-Nirenberg. Our method is based on the K-functionals and allows one to derive self-improving type inequalities. We
Externí odkaz:
http://arxiv.org/abs/2309.02597