e-mail: dms at pdmi dot ras dot ru; d.m.stolyarov at spbu dot ru
e-mail for students: dmsforstudents at google dot com
My thesis (in Russian)
Mathematicians from St. Petersburg and their theorems
For students:
Mathematical analysis 2, practice class
Papers
Oscillatory integrals
Michael Goldberg, Dmitriy Stolyarov, Restrictions of higher derivatives of Fourier transform, arxiv.org/abs/1809.04159, Transactions of the American Mathematical Society series B 7 (2020), 46–96.
D. M. Stolyarov, Functions whose Fourier transform vanishes on a surface, arxiv.org/abs/1601.04604.
Bellman functions
Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskiy, Sharp multiplicative inequalities with BMO I, Journal of Mathematical Analysis and Applications 492:2, 124479, https://arxiv.org/abs/2001.09454 .
Dmitriy Stolyarov, Pavel Zatitskiy, Sharp transference principle for BMO and A_p, https://arxiv.org/abs/1908.09497.
Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskiy, Ilya Zlotnikov, Sharp moment estimates for martingales with uniformly bounded square functions, https://arxiv.org/abs/2102.11568
Short report: Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskiy, Ilya Zlotnikov, Distribution of martingales with bounded square function, Comptes Rendus Mathematique 357:8 (2019), 671–675.
Haakan Hedenmalm, Dmitriy M. Stolyarov, Vasily I. Vasyunin, Pavel B. Zatitskiy, A sharpening of Holder inequality, arxiv.org/abs/1708.08846, Journal of Functional Analysis 275:5 (2018), 1280–1319.
Paata Ivanisvili, Dmitriy M. Stolyarov, Vasily I. Vasyunin, Pavel B. Zatitskiy, Bellman function for extremal problems in BMO II: evolution, http://arxiv.org/abs/1510.01010, Memoirs AMS 255:1220, 2018.
Dmitriy M. Stolyarov, Pavel B. Zatitskiy, Theory of locally concave functions and its applications to sharp estimates of integral functionals, arxiv.org/abs/1412.5350, Advances in Mathematics 291 (2016), 228–273.
Paata Ivanisvili, Nikolay N. Osipov, Dmitriy M. Stolyarov, Vasily I. Vasyunin, Pavel B. Zatitskiy, Sharp estimates of integral functionals on classes of functions with small mean oscillation, arxiv.org/abs/1412.4749, Comptes Rendus Mathematique 353:12 (2015), 1081–1085.
Paata Ivanisvili, Dmitriy M. Stolyarov, Pavel B. Zatitskiy, Bellman VS Beurling: sharp estimates of uniform convexity for $L^p$ spaces, arxiv.org/abs/1405.6229, Algebra i Analiz, 27:2 (2015), 218–231 (in Russian); English translation: St.-Petersburg Mathematics Journal 27 (2016), 333–343.
Alexander A. Logunov, Leonid Slavin, Dmitriy M. Stolyarov, Vasily Vasyunin, Pavel B. Zatitskiy, Weak integral conditions for~$\BMO$, arxiv.org/abs/1309.6780, Proceedings AMS, 143 (2015), 2913–2926.
Paata Ivanishvili, Nikolay N. Osipov, Dmitriy M. Stolyarov, Vasily I. Vasyunin, Pavel B. Zatitskiy, Bellman function for extremal problems in~$\BMO$, arxiv.org/abs/1205.7018, Transactions AMS 368 (2016), 3415–3468;
Short report: Paata Ivanishvili, Nikolay N. Osipov, Dmitriy M. Stolyarov, Vasily I. Vasyunin, Pavel B. Zatitskiy, On Bellman function for extremal problems in~$\BMO$, Comptes Rendus Mathematique, 350:11 (2012), 561–564.
Also see earlier version (in Russian) at www.pdmi.ras.ru/preprint/2011/rus-2011.html
L_1 and L_{\infty}-spaces
Dmitriy Stolyarov, Dimension estimates for vectorial measures with restricted spectrum, https://arxiv.org/abs/2010.14961
Dmitriy Stolyarov, Hardy–Littlewood–Sobolev inequality for p=1, https://arxiv.org/abs/2010.05297
Dmitriy Stolyarov, Weakly canceling operators and singular integrals, https://arxiv.org/abs/2006.11617, to appear in Proceedings of Steklov Mathematical Institute
Dmitriy Stolyarov, Martingale interpretation of weakly cancelling differential operators, https://arxiv.org/abs/1909.00148, Zapiski Nauchnyh Seminarov POMI 480 (2019), 191–198 (in Russian), translated in Journal of Mathematical Sciences (New York) 251:2 (2020), 286–290.
Rami Ayoush, Dmitriy Stolyarov, Michal Wojciechowski, Martingale approach to Sobolev embedding theorems, https://arxiv.org/abs/1811.08137, to appear in Revista Matematica Iberoamericana.
D. M. Stolyarov, Dorronsoro’s theorem and a slight generalisation, arxiv.org/abs/1506.06383 Zapiski nauchn. sem. POMI 434, English translation: Journal of Mathematical Sciences (New York), 215:5, 624–630.
K. Kazaniecki, D. M. Stolyarov, M. Wojciechowski, Anisotropic Ornstein non-inequalities, arxiv.org/abs/1505.05416, Analysis & PDE 10:2 (2017). 351–366.
D. M. Stolyarov, Bilinear embedding theorems for differential operators in $\mathbb{R}^2$, arxiv.org/abs/1406.2009, Zapiski nauchn. sem. POMI, 424 (2014), 210–235 (Russian); English translation: Journal of Mathematical Sciences (New York), 206:5 (2015), 792–807.
D. M. Stolyarov, M. Wojciechowski, Dimension of gradient measures, arxiv.org/abs/1402.4443, Comptes Rendus Mathematique, 352:10 (2014), 791–795
S. V. Kislyakov, D. V. Maksimov, D. M. Stolyarov, Differential expression with mixed homogeneity and spaces of smooth functions they generate in arbitrary dimension, Journal of Functional Analysis, 269:10 (2015), 3220–3263;
Short report: S. V. Kislyakov, D. V. Maksimov, D. M. Stolyarov, Spaces of smooth functions generated by nonhomogeneous differential expressions, Functional Analysis and its Applications, 47:2 (2013), 157–159,
Also see earlier preprint (which differs from the submitted version): S. V. Kislyakov, D. V. Maksimov, D. M. Stolyarov, Differential expressions with mixed homogeneity and spaces of smooth functions they generate, arxiv.org/abs/1209.2078.
D. M. Stolyarov, New correction theorems in the light of Littlewood–Paley–Rubio de Francia inequality, arxiv.org/abs/1105.6215v1, Zap. nauchn. sem. POMI, 389 (2011), 232–251 (Russian); English translation: Journal of Mathematical Sciences (New York), 182:5 (2012), 714–723.
Regularized traces
A. I. Nazarov, D. M. Stolyarov, P. B. Zatitskiy, Tamarkin equiconvergence theorem and trace formula revisited, arxiv.org/abs/1210.8097, Journal of Spectral Theory, 4:2 (2014), 365–389.
A. I. Nazarov, D. M. Stolyarov, P. B. Zatitskiy, On formula of regularized traces, arxiv.org/abs/1103.5775, DAN, 442:2 (2012), 162–165 (Russian); English translation: Doklady Mathematics, 85:1 (2012), 29–32.
There were earlier versions of this paper, they can be found at www.mathsoc.spb.ru/preprint/2010/index.html and www.mathsoc.spb.ru/preprint/2011/index.html .
Miscellaneous
D. Stolyarov, D. Yarcev, Fractional integration for irregular martingales, https://arxiv.org/abs/2009.05293, to appear in Tohoku Mathematical Journal.
R. Ayoush, D. Stolyarov, M. Wojciechowski, Hausdorff dimension of measures with arithmetically restricted spectrum, to appear in Annales Academiae Scientiarum Fennicae Mathematica, https://arxiv.org/abs/2002.06443.
W. Smith, D. M. Stolyarov, A. Volberg, Uniform approximation of Bloch functions and the boundedness of the integration operator on $H^{\infty}$, arxiv.org/abs/1604.05433, Advances in Mathematics 314 (2017), 185–202.
D. M. Stolyarov, V. I. Vasyunin, P. B. Zatitskiy, Monotonic rearrangement of functions with small mean oscillation, arxiv.org/abs/1506.00502, Studia Mathematica 231:3 (2015), 257–268.
A. L. Glazman, P. B. Zatitski, A. S. Sivatski, D. M. Stolyarov, Forms of higher degree over certain fields, Zap. nauchn. sem. POMI (Journal of Mathematical Sciences), 394 (2011), 209–217.
F. V. Petrov, D. M. Stolyarov and P. B. Zatitskiy, On embeddings of finite metric spaces in $l_{\infty}^n$, arxiv.org/abs/0903.4355, Mathematika, 56:1 (2010), 135–139.
A. L. Tulupyev, D. M. Stolyarov, M. V. Mentyukov, A representation for local and global structures of an algebraical Bayesian network in java applications, Trudy SPIIRAN 5 (2007), 71–99, (Russian).
Notes
(these notes usually include proofs of well-known statements or similar things I write down for myself)
Uniform measure (a short proof that the Kowalski–Preiss measure is uniform)
Gluing functions: on a reasoning by Fedor Nazarov (in Russian)
Ito seminar notes (Achtung!: handwriting in Russian)
Previous teaching
Mathematical analysis practice class 1, Fall 2020
Analysis practice class 3, Fall 2019
Analysis practice class 4, Spring 2019
Quasiregular mappings, Spring 2019
Additive combinatorics, Fall 2018
Practice class, Analysis 3, Fall 2018
Practice class, Analysis 2, Spring 2018
