Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Zatitskiy, Pavel"'
Autor:
Stolyarov, Dmitriy, Zatitskiy, Pavel
We prove that certain Bellman functions of several variables are the minimal locally concave functions. This generalizes earlier results about Bellman functions of two variables.
Comment: 30 pages, 10 figures
Comment: 30 pages, 10 figures
Externí odkaz:
http://arxiv.org/abs/2204.12719
Publikováno v:
Journal of Mathematical Analysis and Applications, Volume 515, Issue 2, (2022), 126430
We find the best possible constant $C$ in the inequality $$\|\varphi\|_{L^r}^{\phantom{\frac{p}{r}}}\leq C\|\varphi\|_{L^p}^{\frac{p}{r}}\|\varphi\|_{\mathrm{BMO}}^{1-\frac{p}{r}}$$ for all possible values of parameters $p$ and $r$ such that $1 \le p
Externí odkaz:
http://arxiv.org/abs/2111.05565
Publikováno v:
Mathematische Zeitschrift, Volume 302, Issue 1, (2022), 181--217
We provide sharp bounds for the exponential moments and $p$-moments, $1\leqslant p \leqslant 2$, of the terminate distribution of a martingale whose square function is uniformly bounded by one. We introduce a Bellman function for the corresponding ex
Externí odkaz:
http://arxiv.org/abs/2102.11568
We find the best possible constant $C$ in the inequality $\|\varphi\|_{L^r}\leq C\|\varphi\|_{L^p}^{\frac{p}{r}}\|\varphi\|_{\mathrm{BMO}}^{1-\frac{p}{r}}$, where $2 \leq r$ and $p < r$. We employ the Bellman function technique to solve this problem
Externí odkaz:
http://arxiv.org/abs/2001.09454
Autor:
Stolyarov, Dmitriy, Zatitskiy, Pavel
We provide a version of the transference principle. It says that certain optimization problems for functions on the circle, the interval, and the line have the same answers. In particular, we show that the sharp constants in the John--Nirenberg inequ
Externí odkaz:
http://arxiv.org/abs/1908.09497
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 November 2022 515(2)
Publikováno v:
J. Funct. Anal. 275 no. 5 (2018), 1280-1319
We strengthen H\"older's inequality. The new family of sharp inequalities we obtain might be thought of as an analog of Pythagorean theorem for the $L^p$ spaces. Our reasonings rely upon Bellman functions of four variables.
Comment: 30 pages
Comment: 30 pages
Externí odkaz:
http://arxiv.org/abs/1708.08846
Autor:
Stolyarov, Dmitriy, Zatitskiy, Pavel
Publikováno v:
In Journal of Functional Analysis 15 September 2021 281(6)
In the paper "Bellman function for extremal problems in $\mathrm{BMO}$", the authors built the Bellman function for integral functionals on the $\mathrm{BMO}$ space. The present paper provides a development of the subject. We abandon the majority of
Externí odkaz:
http://arxiv.org/abs/1510.01010
Publikováno v:
Studia Mathematica 231:3 (2015), 257--268
We obtain sharp bounds for the monotonic rearrangement operator from "dyadic-type" classes to "continuous". In particular, for the $\mathrm{BMO}$ space and Muckenhoupt classes. The idea is to connect the problem with a simple geometric construction n
Externí odkaz:
http://arxiv.org/abs/1506.00502