Исследовательская лаборатория им. П. Л. Чебышева

Dmitriy Stolyarov

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 CV

My thesis (in Russian)

Mathematicians from St. Petersburg and their theorems

For students:

Практика по математическому анализу, часть 3

Анализ на гладких многообразиях,

Papers

Fourier analysis

Dmitriy Stolyarov, On Fourier multipliers with rapidly oscillating symbols, https://arxiv.org/abs/2203.04881, Algebra i analiz 35:4 (2023), 167—182; to be translated in St. Petersburg Math. Journal.

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

Egor Dobronravov, Dmitriy Stolyarov, Pavel Zatitskii, New Bellman induction and BMO, https://arxiv.org/abs/2404.01707

Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskii, Martingale transforms of bounded random variables and indicator functions of events, https://arxiv.org/abs/2310.02362

Paata Ivanisvili, Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskii, Bellman functions on simple non-convex domains in the plane, https://arxiv.org/abs/2305.03523

Dmitriy Stolyarov, Pavel Zatitskiy, On locally concave functions on simplest non-convex domains, https://arxiv.org/abs/2204.12719, Zapiski Nauchnyh Seminar POMI 512 (2022), 40—87 (in Russian).

Dmitriy Stolyarov, On Φ-inequalities for martingale fractional integration and their Bellman functions, https://arxiv.org/abs/2107.09336, Michigan Math. Journal 74:3 (2024), 509—526.

Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskiy, Sharp multiplicative inequalities with BMO I, Journal of Mathematical Analysis and Applications 492:2 (2020), 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, Journal of Functional Analysis, 281:6 (2021), 109085.

Dmitriy Stolyarov, Vasily Vasyunin, Pavel Zatitskiy, Ilya Zlotnikov, Sharp moment estimates for martingales with uniformly bounded square functions, https://arxiv.org/abs/2102.11568, Mathematische Zeitschrift 302 (2022), 187—217.

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, Maz’ya’s $\Phi$-inequalities on domains, https://arxiv.org/abs/2407.14052

Daniel Spector, Dmitriy Stolyarov, On dimension stable spaces of measures, https://arxiv.org/2405.10728.

Rami Ayoush, Dmitriy Stolyarov, Michał Wojciechowski, Alberti’s type rank one theorem for martingales, https://arxiv.org/abs/2307.11381.

Dmitriy Stolyarov, Trace inequalities for Sobolev martingales, https://arxiv.org/abs/2211.13456 .

Dmitriy Stolyarov, Fractional integration of measures: Maz’ya’s $\Phi$-inequalities, https://arxiv.org/abs/2109.08014, to appear in Annali della Scuola normale superiore di Pisa.

Bogdan Raita, Daniel Spector, Dmitriy Stolyarov, A trace inequality for solenoidal charges, https://arxiv.org/abs/2109.02029, Potential Analysis 59 (2023), 2093—2104.

Dmitriy Stolyarov, Dimension estimates for vectorial measures with restricted spectrum, https://arxiv.org/abs/2010.14961, Journal of Functional Analysis 284:1 (2023), 109735.

Dmitriy Stolyarov, Hardy—Littlewood—Sobolev inequality for p=1, https://arxiv.org/abs/2010.05297, Sbornik Mathematics 213:6 (2022), 125—174.

Dmitriy Stolyarov, Weakly canceling operators and singular integrals, https://arxiv.org/abs/2006.11617, Proceedings of Steklov Mathematical Institute 312 (2021), 249—260.

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, Sobolev martingales, https://arxiv.org/abs/1811.08137, Revista Matematica Iberoamericana 37:4 (2021), 1225—1246.

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.

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, On embedding of Besov spaces of zero smoothness into Lorentz spaces, https://arxiv.org/abs/2301.06370, to appear in Proceedings of Steklov Mathematical Institute.

D. Azagra, D. Stolyarov, Inner and outer approximation of convex hyper surfaces. When is it possible?, https://arxiv.org/abs/2204.07498, Nonlinear Analysis 230 (2023), 113225.

D. Stolyarov, D. Yarcev, Fractional integration for irregular martingales, https://arxiv.org/abs/2009.05293, Tohoku Mathematical Journal 74:2 (2022), 253—261.

R. Ayoush, D. Stolyarov, M. Wojciechowski, Hausdorff dimension of measures with arithmetically restricted spectrum, https://arxiv.org/abs/2002.06443, Annales Academiae Scientiarum Fennicae Mathematica, 46:1 (2021), 537—551.

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.

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.

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)

Dual approach to Gagliardo—Nirenberg—Sobolev inequality

Uniform measure (a short proof that the Kowalski—Preiss measure is uniform)

Approximation of analytic functions on strips and semi-strips (addendum to my paper with Smith and Volberg)

Gluing functions: on a reasoning by Fedor Nazarov (in Russian)

Latala’s inequality

Rank-one convexity

Dorronsoro’s theorem

Ito seminar notes (Achtung!: handwriting in Russian)

Convexity in Banach spaces: B-convexity, K-convexity, Pisier’s great theorem, the Beurling—Kato theorem (handwriting in Russian)

Previous teaching