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Krotov, Veniamin Grigoryevich

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Total publications: 33
Scientific articles: 33
Presentations: 1

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This page:6440
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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: http://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.

http://www.mathnet.ru/eng/person17664
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/207334
http://elibrary.ru/author_items.asp?spin=2828-3672
http://www.scopus.com/authid/detail.url?authorId=7006670486

Publications in Math-Net.Ru
2020
1. 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  mathnet; Math. Notes, 107:2 (2020), 257–263  isi  scopus
2015
2. V. G. Krotov, A. I. Porabkovich, “Estimates of $L^p$-Oscillations of Functions for $p>0$”, Mat. Zametki, 97:3 (2015),  407–420  mathnet  mathscinet  zmath  elib; Math. Notes, 97:3 (2015), 384–395  isi  scopus
2013
3. 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  mathnet  mathscinet  elib; J. Math. Sci., 209:1 (2015), 108–114  scopus
4. 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  mathnet  mathscinet  zmath  elib; Math. Notes, 93:2 (2013), 217–223  isi  elib  scopus
2012
5. V. G. Krotov, “Criteria for compactness in $L^p$-spaces, $p\ge0$”, Mat. Sb., 203:7 (2012),  129–148  mathnet  mathscinet  zmath  elib; Sb. Math., 203:7 (2012), 1045–1064  isi  scopus
6. I. A. Ivanishko, V. G. Krotov, A. I. Porabkovich, “A generalization of Campanato–Meyers' theorem”, Tr. Inst. Mat., 20:2 (2012),  30–35  mathnet
2011
7. 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  mathnet  mathscinet; Math. Notes, 89:1 (2011), 156–159  isi  scopus
2009
8. I. A. Ivanishko, V. G. Krotov, “Compactness of Embeddings of Sobolev Type on Metric Measure Spaces”, Mat. Zametki, 86:6 (2009),  829–844  mathnet  mathscinet  zmath; Math. Notes, 86:6 (2009), 775–788  isi  scopus
2008
9. 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, 5,  55–66  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 52:5 (2008), 47–57
2006
10. V. G. Krotov, L. V. Smovzh, “Weighted estimates for tangential boundary behaviour”, Mat. Sb., 197:2 (2006),  57–74  mathnet  mathscinet  zmath  elib; Sb. Math., 197:2 (2006), 193–211  isi  scopus
11. I. A. Ivanishko, V. G. Krotov, “Generalized Poincaré–Sobolev inequality on metric spaces”, Tr. Inst. Mat., 14:1 (2006),  51–61  mathnet
2004
12. 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  mathnet  mathscinet  zmath; Math. Notes, 75:4 (2004), 542–552  isi
2003
13. V. G. Krotov, “When is an Orthogonal Series a Fourier Series?”, Mat. Zametki, 74:1 (2003),  139–142  mathnet  mathscinet  zmath; Math. Notes, 74:1 (2003), 132–135  isi  scopus
2000
14. V. G. Krotov, “Tangential boundary behavior of functions of several variables”, Mat. Zametki, 68:2 (2000),  230–248  mathnet  mathscinet  zmath; Math. Notes, 68:2 (2000), 201–216  isi
1997
15. 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  mathnet  mathscinet  zmath; Math. Notes, 62:4 (1997), 439–448  isi
1991
16. 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  mathnet  mathscinet  zmath; Dokl. Math., 44:1 (1992), 36–39
17. V. G. Krotov, “On the smoothness of universal Marcinkiewicz functions and universal trigonometric series”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, 8,  26–31  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 35:8 (1991), 24–28
1990
18. 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  mathnet  mathscinet  zmath; Math. USSR-Izv., 37:2 (1991), 303–320
1989
19. 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  mathnet  mathscinet  zmath; Math. Notes, 45:2 (1989), 122–128  isi
20. V. G. Krotov, “Estimates of maximal operators connected with the boundary behaviour and their applications”, Trudy Mat. Inst. Steklov., 190 (1989),  117–138  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 190 (1992), 123–144
1988
21. V. G. Krotov, “Boundary behavior of fractional integrals of holomorphic functions in the unit ball in $C^N$”, Izv. Vyssh. Uchebn. Zaved. Mat., 1988, 4,  73–75  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 32:4 (1988), 104–108
1987
22. 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  mathnet  mathscinet  zmath; Math. USSR-Sb., 62:2 (1989), 403–419
23. 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  mathnet  zmath; Proc. Steklov Inst. Math., 180 (1989), 164–165
1982
24. V. G. Krotov, “Unconditional basicity of the Haar system in the spaces $\Lambda_\omega^1$”, Mat. Zametki, 32:5 (1982),  675–684  mathnet  mathscinet  zmath; Math. Notes, 32:5 (1982), 822–827  isi
25. V. G. Krotov, “On differentiability of functions in $L^p$, $0<p<1$”, Mat. Sb. (N.S.), 117(159):1 (1982),  95–113  mathnet  mathscinet  zmath; Math. USSR-Sb., 45:1 (1983), 101–119
1981
26. 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  mathnet  mathscinet  zmath
1978
27. 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  mathnet  mathscinet  zmath; Math. Notes, 23:5 (1978), 376–382
1977
28. 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  mathnet  mathscinet  zmath; Math. USSR-Izv., 11:1 (1977), 205–218
1976
29. 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  mathnet  mathscinet  zmath
1975
30. 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, 10,  33–46  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 19:10 (1975), 27–39
31. 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  mathnet  mathscinet  zmath; Math. USSR-Sb., 27:3 (1975), 355–374
1974
32. 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  mathnet  mathscinet  zmath
1973
33. 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  mathnet  mathscinet  zmath; Math. Notes, 14:2 (1973), 665–670

Presentations in Math-Net.Ru
1. 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   

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