Persons: Krotov, Veniamin Grigoryevich

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Krotov, Veniamin Grigoryevich

$Krotov, Veniamin Grigoryevich$

Professor

Doctor of physico-mathematical sciences (1990)

Speciality:

01.01.01 (Real analysis, complex analysis, and functional analysis)

Birth date:

7.05.1949

E-mail:

Website:

https://www.bsu.by/ru/main.aspx?guid=19521

Keywords:

inequalities in approximation theory, Sobolev spaces, embedding theorems, Hardy spaces, boundary behavior of solutions of boundary values problems, fine properties of functions, exceptional sets.

UDC:

517.51, 517.518, 517.53, 517.95, 517.98, 517.5, 517, 517.552, 517.518.22

MSC:

26Bxx, 26Dxx, 30Exx, 42Bxx, 42Axx, 32A40, 26A33, 32A35

Subject:

harmonic analysis; function spaces; approximation of functions; analysis on metric measure spaces

Biography

Graduated from Faculty of Mathematics and Mechanics of Odessa State University in 1971 (department of mathematical analysis). Ph.D. thesis was defended in 1974 ("The coefficients of espansions in functional spaces and representation of measurable functions by series"). D.Sci. thesis was defended in 1990 ("The boundary behavior and differential properties of smooth functions of several variables").

Main publications:

E. A.Storozhenko, V. G. Krotov, P. Osvald. Pryamye i obratnye teoremy tipa Dzheksona v prostranstvakh $L^p$, $0<p<1$ // Matematicheskii sbornik, 1975, 98(110), 3, 395–415.
V. G. Krotov. O differentsiruemosti funktsii iz $L^p$, $0<p<1$ // Matematicheskii sbornik, 1982, 117(159), 95–113.
V. G. Krotov. O gladkosti primitivnykh N. N. Luzina i o teoremakh D. E. Menshova i N. K. Bari // Matematicheskii sbornik, 1987, 134(176), 3, 404–420.
V. G. Krotov. Otsenki dlya maksimalnykh operatorov, svyazannykh s granichnym povedeniem, i ikh prilozheniya // Trudy Matematicheskogo instituta im. V. A. Steklova AN SSSR, 1989, 190, 117–138.
V. G. Krotov. O kasatelnom granichnom povedenii funktsii mnogikh peremennykh // Matematicheskie zametki, 2000, 68, 2, 230–248.

https://www.mathnet.ru/eng/person17664

List of publications on Google Scholar

https://mathscinet.ams.org/mathscinet/MRAuthorID/207334

https://elibrary.ru/author_items.asp?spin=2828-3672

https://orcid.org/0000-0003-4053-9919

https://www.scopus.com/authid/detail.url?authorId=7006670486

	Publications in Math-Net.Ru	Citations
	2024
1.	V. G. Krotov, “Marcinkiewicz's interpolation theorem for Hardy-type spaces and its applications”, Mat. Sb., 215:8 (2024), 95–119 ; Sb. Math., 215:8 (2024), 1091–1113
	2023
2.	V. G. Krotov, “Marcinkiewicz Interpolation Theorem for Spaces of Hardy Type”, Mat. Zametki, 113:2 (2023), 311–315 ; Math. Notes, 113:2 (2023), 306–310	2
3.	V. G. Krotov, “Interpolation of Operators in Hardy-Type Spaces”, Trudy Mat. Inst. Steklova, 323 (2023), 181–195 ; Proc. Steklov Inst. Math., 323 (2023), 173–187	1
	2021
4.	G. A. Karagulyan, I. N. Katkovskaya, V. G. Krotov, “The Fatou Property for General Approximate Identities on Metric Measure Spaces”, Mat. Zametki, 110:2 (2021), 204–220 ; Math. Notes, 110:2 (2021), 196–209
	2020
5.	I. N. Katkovskaya, V. G. Krotov, “On the Continuity of Best Approximations by Constants on Balls in Metric Measure Spaces”, Mat. Zametki, 107:2 (2020), 221–228 ; Math. Notes, 107:2 (2020), 257–263
	2015
6.	V. G. Krotov, A. I. Porabkovich, “Estimates of $L^p$-Oscillations of Functions for $p>0$”, Mat. Zametki, 97:3 (2015), 407–420 ; Math. Notes, 97:3 (2015), 384–395	7
	2013
7.	V. G. Krotov, M. A. Prokhorovich, “Functions from Sobolev and Besov spaces with maximal Hausdorff dimension of the exceptional Lebesgue set”, Fundam. Prikl. Mat., 18:5 (2013), 145–153 ; J. Math. Sci., 209:1 (2015), 108–114	1
8.	M. G. Grigoryan, V. G. Krotov, “Luzin's Correction Theorem and the Coefficients of Fourier Expansions in the Faber–Schauder System”, Mat. Zametki, 93:2 (2013), 172–178 ; Math. Notes, 93:2 (2013), 217–223	11
	2012
9.	V. G. Krotov, “Criteria for compactness in $L^p$-spaces, $p\geqslant0$”, Mat. Sb., 203:7 (2012), 129–148 ; Sb. Math., 203:7 (2012), 1045–1064	18
10.	I. A. Ivanishko, V. G. Krotov, A. I. Porabkovich, “A generalization of Campanato–Meyers' theorem”, Tr. Inst. Mat., 20:2 (2012), 30–35	1
	2011
11.	V. G. Krotov, M. A. Prokhorovich, “The Rate of Convergence of Steklov Means on Metric Measure Spaces and Hausdorff Dimension”, Mat. Zametki, 89:1 (2011), 145–148 ; Math. Notes, 89:1 (2011), 156–159	7
	2009
12.	I. A. Ivanishko, V. G. Krotov, “Compactness of Embeddings of Sobolev Type on Metric Measure Spaces”, Mat. Zametki, 86:6 (2009), 829–844 ; Math. Notes, 86:6 (2009), 775–788	18
	2008
13.	V. G. Krotov, M. A. Prokhorovich, “The Luzin approximation of functions from the classes $W^p_\alpha$ on metric spaces with measure”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 5, 55–66 ; Russian Math. (Iz. VUZ), 52:5 (2008), 47–57	9
	2006
14.	V. G. Krotov, L. V. Smovzh, “Weighted estimates for tangential boundary behaviour”, Mat. Sb., 197:2 (2006), 57–74 ; Sb. Math., 197:2 (2006), 193–211
15.	I. A. Ivanishko, V. G. Krotov, “Generalized Poincaré–Sobolev inequality on metric spaces”, Tr. Inst. Mat., 14:1 (2006), 51–61	8
	2004
16.	V. G. Krotov, I. N. Katkovskaya, “Strong-Type Inequality for Convolution with Square Root of the Poisson Kernel”, Mat. Zametki, 75:4 (2004), 580–591 ; Math. Notes, 75:4 (2004), 542–552	4
	2003
17.	V. G. Krotov, “When is an Orthogonal Series a Fourier Series?”, Mat. Zametki, 74:1 (2003), 139–142 ; Math. Notes, 74:1 (2003), 132–135
	2000
18.	V. G. Krotov, “Tangential boundary behavior of functions of several variables”, Mat. Zametki, 68:2 (2000), 230–248 ; Math. Notes, 68:2 (2000), 201–216	7
	1997
19.	V. G. Krotov, “An exact estimate of the boundary behavior of functions from Hardy–Sobolev classes in the critical case”, Mat. Zametki, 62:4 (1997), 527–539 ; Math. Notes, 62:4 (1997), 439–448	3
	1991
20.	V. G. Krotov, “A sharp estimate for the boundary behavior of functions in the Hardy–Sobolev classes $H^p_\alpha(B^n)$ in the critical case $\alpha p=n$”, Dokl. Akad. Nauk SSSR, 319:1 (1991), 42–45 ; Dokl. Math., 44:1 (1992), 36–39	1
21.	V. G. Krotov, “On the smoothness of universal Marcinkiewicz functions and universal trigonometric series”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, no. 8, 26–31 ; Soviet Math. (Iz. VUZ), 35:8 (1991), 24–28	4
	1990
22.	V. G. Krotov, “On the boundary behavior of functions in spaces of Hardy type”, Izv. Akad. Nauk SSSR Ser. Mat., 54:5 (1990), 957–974 ; Math. USSR-Izv., 37:2 (1991), 303–320	6
	1989
23.	V. G. Krotov, “Differential properties on the boundary of functions that are holomorphic in the unit ball in $C^N$”, Mat. Zametki, 45:2 (1989), 51–59 ; Math. Notes, 45:2 (1989), 122–128	1
24.	V. G. Krotov, “Estimates of maximal operators connected with the boundary behaviour and their applications”, Trudy Mat. Inst. Steklov., 190 (1989), 117–138 ; Proc. Steklov Inst. Math., 190 (1992), 123–144	9
	1988
25.	V. G. Krotov, “Boundary behavior of fractional integrals of holomorphic functions in the unit ball in $C^N$”, Izv. Vyssh. Uchebn. Zaved. Mat., 1988, no. 4, 73–75 ; Soviet Math. (Iz. VUZ), 32:4 (1988), 104–108	3
	1987
26.	V. G. Krotov, “On the smoothness of Luzin primitives and on theorems of Men'shov and Bari”, Mat. Sb. (N.S.), 134(176):3(11) (1987), 404–420 ; Math. USSR-Sb., 62:2 (1989), 403–419	1
27.	V. G. Krotov, “On differentiability properties of functions in $H^p$ on the boundary of the disk of convergence”, Trudy Mat. Inst. Steklov., 180 (1987), 141–142 ; Proc. Steklov Inst. Math., 180 (1989), 164–165
	1982
28.	V. G. Krotov, “Unconditional basicity of the Haar system in the spaces $\Lambda_\omega^1$”, Mat. Zametki, 32:5 (1982), 675–684 ; Math. Notes, 32:5 (1982), 822–827	1
29.	V. G. Krotov, “On differentiability of functions in $L^p$, $0<p<1$”, Mat. Sb. (N.S.), 117(159):1 (1982), 95–113 ; Math. USSR-Sb., 45:1 (1983), 101–119	9
	1981
30.	V. G. Krotov, “On differentiability of functions in $L^p$ and $H^p$ for $0<p<1$”, Dokl. Akad. Nauk SSSR, 256:6 (1981), 1311–1314
	1978
31.	V. G. Krotov, “Unconditional convergence of Fourier series with respect to the Haar system in the spaces $\Lambda_\omega^p$”, Mat. Zametki, 23:5 (1978), 685–695 ; Math. Notes, 23:5 (1978), 376–382	4
	1977
32.	V. G. Krotov, “Representation of measurable functions by series in the Faber–Schauder system, and universal series”, Izv. Akad. Nauk SSSR Ser. Mat., 41:1 (1977), 215–229 ; Math. USSR-Izv., 11:1 (1977), 205–218	19
	1976
33.	V. G. Krotov, P. Oswald, È. A. Storozhenko, “Direct and inverse theorems of Jackson type in $L^p$ spaces ($0<p<1$)”, Dokl. Akad. Nauk SSSR, 226:1 (1976), 44–47	1
	1975
34.	V. G. Krotov, “Fourier coefficients with respect to a certain orthonormal system that forms a basis in the space of continuous functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 1975, no. 10, 33–46 ; Soviet Math. (Iz. VUZ), 19:10 (1975), 27–39
35.	È. A. Storozhenko, V. G. Krotov, P. Oswald, “Direct and converse theorems of Jackson type in $L^p$ spaces, $0<p<1$”, Mat. Sb. (N.S.), 98(140):3(11) (1975), 395–415 ; Math. USSR-Sb., 27:3 (1975), 355–374	66
36.	V. G. Krotov, “Correction to the paper “Haar series””, Sibirsk. Mat. Zh., 16:2 (1975), 417–418 ; Siberian Math. J., 16:2 (1975), 323
	1974
37.	V. G. Krotov, “Representation of measurable functions by series in the Faber–Schauder system and universal series”, Dokl. Akad. Nauk SSSR, 214:6 (1974), 1258–1261	2
38.	V. G. Krotov, “Continuous functions with monotonically increasing Fourier coefficients in the Haar system”, Sibirsk. Mat. Zh., 15:2 (1974), 439–444 ; Siberian Math. J., 15:2 (1974), 316–320
	1973
39.	V. G. Krotov, “On series with respect to the Faber–Schauder system and with respect to the bases of the space $C[0,1]$”, Mat. Zametki, 14:2 (1973), 185–195 ; Math. Notes, 14:2 (1973), 665–670	2
40.	V. G. Krotov, “Series in the Haar system”, Sibirsk. Mat. Zh., 14:1 (1973), 111–127 ; Siberian Math. J., 14:1 (1973), 78–89

Presentations in Math-Net.Ru

1.	Generalization of Hardy-Littlewood inequalities for Hardy classes V. G. Krotov, I. N. Katkovskaya International Conference “Nonlinear Approximation and Discretization” dedicated to the 70-th anniversary of Professor V.N. Temlyakov November 2, 2023 10:00
2.	On the tangential boundary behavior of functions from Hardy type spaces V. G. Krotov, I. N. Katkovskaya Conference on the Theory of Functions of Several Real Variables, dedicated to the 90th anniversary of O. V. Besov May 31, 2023 10:00
3.	The Fatou property for general approximate identities on metric measure spaces V. G. Krotov International Conference "Approximation Theory and Applications" Dedicated to the 100th Anniversary S. B. Stechkin September 9, 2021 10:00
4.	Тонкие свойства функций из пространств Хайлаша–Cоболева $W^p_{\alpha}$, $p>0$ V. G. Krotov, S. A. Bondarev International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii May 28, 2015 11:40

Organisations

Belarusian State University, Faculty of Mathematics and Mechanics
Belarusian State University, Minsk
Belarusian National Technical University
I. I. Mechnikov Odessa National University
The Academy of Public Administration under the aegis of the President of the Republic of Belarus

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