Zobrazeno 1 - 10
of 139
pro vyhledávání: '"Stolyarov, A. M."'
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
We obtain a necessary and sufficient condition for the operator of integration to be bounded on $H^\infty$ in a simply connected domain. The main ingredient of the proof is a new result on uniform approximation of Bloch functions. This gives a full c
Externí odkaz:
http://arxiv.org/abs/1604.05433
Autor:
Stolyarov, Dmitriy M.
We study the subspaces of $L_p(\mathbb{R}^d)$ that consist of functions whose Fourier transforms vanish on a smooth surface of codimension $1$. We show that a subspace defined in such a manner coincides with the whole $L_p$ space for $p > \frac{2d}{d
Externí odkaz:
http://arxiv.org/abs/1601.04604
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
Publikováno v:
Anal. PDE 10 (2017) 351-366
We investigate existence of a priori estimates for differential operators in $L^1$ norm: for anisotropic homogeneous differential operators $T_1, \ldots , T_{\ell}$, we study the conditions under which the inequality $$ \|T_1 f\|_{L_1(\mathbb{R}^d)}
Externí odkaz:
http://arxiv.org/abs/1505.05416
Publikováno v:
Advances in Mathematics 291 (2016), 228--273
We prove a duality theorem the computation of certain Bellman functions is usually based on. As a byproduct, we obtain sharp results about the norms of monotonic rearrangements. The main novelty of our approach is a special class of martingales and a
Externí odkaz:
http://arxiv.org/abs/1412.5350
Autor:
Ivanisvili, Paata, Osipov, Nikolay N., Stolyarov, Dmitriy M., Vasyunin, Vasily I., Zatitskiy, Pavel B.
Publikováno v:
Comptes Rendus Mathematique 353:12 (2015), 1081--1085
We unify several Bellman function problems into one setting. For that purpose we define a class of functions that have, in a sense, small mean oscillation (this class depends on two convex sets in $\mathbb{R}^2$). We show how the unit ball in the $\m
Externí odkaz:
http://arxiv.org/abs/1412.4749
Autor:
Stolyarov, Dmitriy M.
Publikováno v:
POMI, 424 (2014), 210--235; Journal of Mathematical Sciences, 206:5 (2015), 792--807
We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However, here we stud
Externí odkaz:
http://arxiv.org/abs/1406.2009
Publikováno v:
Algebra i Analiz, 27:2 (2015), 218--231; St.-Petersburg Mathematics Journal 27 (2016), 333--343
We obtain the classical Hanner inequalities by the Bellman function method. These inequalities give sharp estimates for the moduli of convexity of Lebesgue spaces. Easy ideas from differential geometry help us to find the Bellman function using neith
Externí odkaz:
http://arxiv.org/abs/1405.6229