Publications in Refereed Journals

1. Functional and Analytical Properties of a Class of Mappings of Quasiconformal Analysis on Carnot Groups
   Sib. Math. J., 63:2 (2022), 233–261 (with S. K. Vodop'yanov) (link)
2. Vector-valued Sobolev spaces based on Banach function spaces
   Nonlinear Analysis, 211 (2021) (link, arxiv)
3. Sobolev space of functions valued in a monotone Banach family.
   Journal of Mathematical Analysis and Applications, 492 (2020) (with А. Menovschikov) (link, arxiv )
4. On Changing Variables in Lp-Spaces with Distributed-Microstructure.
   Russian Mathematics, 64:3 (2020), 82--86 (with А. Menovschikov) (link)
5. The Composition Operator on Mixed-Norm Lebesgue Spaces.
   Math Notes, 105:5-6 (2019), 812--817 (with А. Menovschikov) (link)
6. Bounded operators on mixed Lebesgue spaces.
   Complex Analysis and Operator Theory (with А. Menovschikov) (link, arxiv )
7. On measurability of Banach indicatrix
   Colloquium Mathematicum, 153 (2018), 97--101. (arxiv, pdf)
8. Bounded composition operator on Lorentz spaces
   Math Notes, 102:6 (2017), 763--769 (link, arxiv)
9. Operators of Change of Variables in Weighted Sobolev Spaces on Carnot Groups
   J Math Sci, (2017), 1-7 (link, pdf)
10. Differentiation of a convolution on the roto-translation group
    Math Notes, 101:1 (2017), 126-130 (with M. Tryamkin)
11. Composition operators in weighted Sobolev spaces on the Carnot group
    Sib. Math. J., 56:6 (2015), 1042-1059 (link, pdf)
12. Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings
    Sib. Math. J., 56:5 (2015), 789-821 (with S. K. Vodop'yanov) (link, pdf)
13. Isomorphisms of Sobolev spaces on Carnot groups and metric properties of mappings
    Dokl. Math., 92:2 (2015), 532-536 (with S. K. Vodop'yanov) (link, pdf)
14. Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings
    Sib. Math. J., 55:5 (2014), 817-848 (with S. K. Vodop'yanov) (link, pdf)

Work in Progress

1. Weak differentiability of metric space valued Sobolev maps (with P. Creutz)
   (arxiv)
2. Brownian path preserving mappings on the Heisenberg group
   (arxiv)
3. An approach to metric space valued Sobolev maps via weak* derivatives (with P. Creutz)
   (arxiv)
4. Mixed operators on $L_p$-direct integrals (with А. Menovschikov)
   (arxiv)

Lecture notes

• Теория функций комплексного переменного (pdf)
• Комплексные числа и функции (pdf)
• Основы комплексного анализа (pdf)
• Элементы Фурье анализа (pdf)

Thesis

• Операторы композиции в пространствах Соболева на группе Карно (pdf)