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Krotov Veniamin

Krotov VeniaminKrotov Veniamin
head of departament of function theory

ADDRESS:
Departament of Mathematical Methods in Control Theory,
Mathematics and Mechanics Faculty,
Belorussian State University,
Nesavisimosti av., 4,
MINSK, 220030,
BELARUS

PHONE: +-375-17-2095367

E-mail: krotov+AEA-bsu.by, vkrotov+AEA-cosmostv.by

Born 7 may 1949 in Moscow

Graduated from the mechanical and mathematicfl faculty of the Odessa state university, 1971 (Ukraine, ex. USSR) and postgraduate study on the department of mathematical analysis of the Odessa state university (1974).

PHD thesis +ACI-Coefficients of expansions with respect to basis of functional spaces and representation of measurabe functions by series+ACI- (Odessa state university, 1974).

Habilitation Thesis (Degree of Dr.Hab.) +ACI-Boundary behavior and differential properties of smooth functions of several variables+ACI- (Institute of mathematics, NAS Ukraine, 1990).

Scientific interest

  • harmonic analysis
  • approximation theory
  • analysis on metric measure spaces
  • function spaces
  • boundary value problems for partial differential equations

My page on Math-Net.ru

http://www.mathnet.ru/php/person.phtml?+ACY-personid+AD0-17664+ACY-option+AF8-lang+AD0-eng

40. V.G.Krotov, M.A.Prokhorovich The Rate of Convergence of Steklov Means on Metric Measure Spaces and Hausdorff Dimension, Math.Notes, 2011, v.89, No.1, p.156-159
http://www.springerlink.com/content/4843022382m6q175/

39. V.G.Krotov, Quantitative form of Luzin C-property, Ukrainian Math. Journal, 2010, v. 62, No 3, p. 441-451
http://www.springerlink.com/content/e242447m43w46743/

38. I.A.Ivanishko, V.G.Krotov, Compactness of imbeddings of Sobolev type on metric measure spaces, Matematicheskie Zametki, 2009, Т.86, №6, C. 829–844. (in Russian, English transl. in Mathematical Notes, 2009, Vol. 86, No. 6, pp. 775–788).
http://www.springerlink.com/content/l0q5710h2771401g/

37. V.G.Krotov, M.A.Prohorovich, Luzin approximation for Sobolev classes on metric measure spaces, Izv.
Vyssh. Uchebn. Zaved. Mat. 2008, No. 5, P.55-66 (in Russian, English transl. in Russian Mathematics (Iz. VUZ), 2008, Vol. 52, No. 5, P. 47–57). http://www.springerlink.com/content/t72m6xk9357t36k2/

36. V.G.Krotov, Weighted Lp-inequalities for sharp-maximal functions on metric measure spaces, Izvestiya Natsionalnoi
Akademii Nauk Armenii. Matematika, 2006, V.41, No.2, P.27-42 (in Russian, English transl. in Journal of Contemporary
Mathematical Analysis (Armenian Academy of Sciences), 2006, V.41, No.2).

35. V.G.Krotov, L.V. Smovzh, Weighted estimates for tangential boundary behaviour, Matematicheskij Sbornik, 2006, V.197,
No.2, P.57–74 (in Russian, English transl. in Sbornik Mathematics, 2006, V.197, No.2, P.193–211).
http://www.turpion.org/php/paper.phtml?journal_id=sm&paper_id=3753

34. I.A.Ivanishko, V.G.Krotov, Generalized Poincare-Sobolev inequality on metric spaces, Trudy Inst.Mat. NAN Belarus, 2006,
V.14, No.1, P.51-61 (in Russian).

33. V.G.Krotov, Weighted Lp-inequalities for Sharp-Maximal Functions, Doklady Rossijskoi Akademii Nauk, 2005, V.404, No.2,
P.155–158 (in Russian, English transl. in Doklady Mathematics, 2005, V.72, No.2, P.684–686).
http://www.maikonline.com/maik/showArticle.do?auid=VAEEQZJEWI

32. I.N.Katkovskaya, V.G.Krotov, Strong-type inequality for convolution with square root of the Poisson kernel, Matematicheskie Zametki, 2004, V.75,
No.4, P.580-591. (in Russian, English transl. in Mathematical Notes, vol. 75, no. 4, 2004, pp. 542–552.).
http://www.springerlink.com/content/gg3x56551w980713/

31. V.G.Krotov, When is an Orthogonal Series a Fourier Series, Matematicheskie Zametki, 2003, V.74, No.1, P.139–142 (in
Russian, English transl. in Mathematical Notes, V. 74, no. 1, 2003, pp. 132–135).
http://www.springerlink.com/content/m8167513845gg203/

30. V.G.Krotov, Tangential boundary behavior of functions of several variables, Matematicheskie Zametki, 2000, V.68,
No.2), P.230–248 (in Russian, English transl. in Math. Notes, 2000, V.68, No.2, P.201-216).
http://www.springerlink.com/content/v8g5542780267705/

29. V.G.Krotov, An exact estimate of the boundary behavior of functions from Hardy-Sobolev classes in the critical case,
Matematicheskie Zametki, 1997, V.62, No.4, P.527–539 (in Russian, English transl. in Math. Notes, 1997, V.62, No.4, P.439-448).
http://www.springerlink.com/content/9502k48142574l54/

28. V.G.Krotov, Inequalities for Peano maximal operators in the ball, Trudy Inst. Mat. NAN of Belarus, Papers dedicated to
60-birthday of professor V.G.Sprindzsuk (1936-1987), Minsk, 1997, P. 64-75 (in Russian).

27. V.G.Krotov, On smoothness of universal Marcinkiewicz functions and universal trigonometric series, Izv. Vyssh.
Uchebn. Zaved. Mat.1991, No.8, P.26-31 (in Russian, English transl. in Soviet Math. (Izv. VUZ)).
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ivm&paperid=5131&option_lang=eng

26. V.G.Krotov, Sharp estimate of boundary behavior of functions from Hardy-Sobolev spaces in critical case ap=n, Doklady
Akademii Nauk USSR, 1991, V.319, No.1, P.42-45 (in Russian, English transl. in Math. USSR Doklady).

25. V.G.Krotov, On boundary behavior of functions from Hardy type spaces, Izvestija Akademii Nauk USSR, Ser. mat., 1990,
V.54, No.5, P.957-974 (in Russian, English transl. in Math. USSR Izvestija).
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=1057&option_lang=eng
http://www.turpion.org/php/paper.phtml?journal_id=im&paper_id=2065&year_id=1991&volume=37&issue_id=2&fpage=303&lpage=320

24. V.G.Krotov, Estimates for maximal operators connected with boundary behavior, and their applications, Trudy Mat. Inst.
Steklov, 1989, V.190, P.117–138 (in Russian, English transl. in Proc. Steklov Inst. Math., 1989, V.190).
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tm&paperid=1774&option_lang=eng

23. V.G.Krotov, Differential properties on the boundary of functions that are holomorphic in the unit ball in CN,
Matematicheskie Zametki, 1989, V.45, No.2, P.51-59 (in Russian, English transl. in Math. Notes, 1989, V.45, No.2).
http://www.springerlink.com/content/qm6082k867077q10/

22. V.G.Krotov, On the boundary behaviour of fractional integrals of holomorphic functions on the unit ball of CN, Izv.
Vyssh. Uchebn. Zaved. Mat., 1988, No.4, 73–75 (in Russian, English transl. in Soviet Math. (Izv. VUZ), 1988, V.32).

21. V.G.Krotov, On smoothness of Luzin primitives and on Menshov and Bari theorems, Matematicheskij Sbornik, 1987, V.134,
No.3, P.404-420 (in Russian, English transl. in Math. USSR Sbornik, 1987, V.134, No.3).
http://www.mathnet.ru/php/journal.phtml?wshow=paper&jrnid=sm&paperid=2767&year=1987&volume=176&issue=3&fpage=404&lpage=420&option_lang=eng
http://www.turpion.org/php/paper.phtml?journal_id=sm&paper_id=3246&year_id=1989&volume=62&issue_id=2&fpage=403&lpage=419

20. V.G.Krotov, E.A.Storozenko, On best approximations and derivatives of analytic functions from Hardy classes, In
"Approximation functions theory", Academia nauk USSR, Ufa, 1987 (in Russian).

19. V.G.Krotov, On differential properties of boundary functions of Hardy classes, Mathematische Nachrichten, 1986, V.126,
P.241-253.
http://www3.interscience.wiley.com/journal/113457966/abstract

18. V.G.Krotov, On differential properties of boundary functions of Hardy classes, Doklady Akademii Nauk Ukraine, Ser.A,
1984, No.6, P.15-18 (in Russian).

17. V.G.Krotov, Unconditional basicity of the Haar system in the spaces Hw, Matematicheskie Zametki, 1982, V.32, No.5,
P.675-684 (in Russian, English transl. in Math. Notes, 1982, V.32, No.5).
http://www.springerlink.com/content/k0gk37052u611u6n/

16. V.G.Krotov, On differentiability of functions in Lp, 0<p<1, Matematicheskij Sbornik, 1982, V.117, No.1, P. 95-113 (in
Russian, English transl. in Math. USSR Sbornik, 1983, V.45, No.1).
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sm&paperid=2184&option_lang=eng
http://www.turpion.org/php/paper.phtml?journal_id=sm&paper_id=2589&year_id=1983&volume=45&issue_id=1&fpage=101&lpage=119

15. V.G.Krotov, On differentiability of functions in Lp, 0<p<1, Doklady Akademii Nauk USSR, 1981, V.256, No.6, P.1311-1314
(in Russian, English transl. in Math. USSR Doklady).

14. A.V.Bakhshetsian, V.G.Krotov, On universal series in Schauder systems, Izvestija Akademii Nauk Armenian, 1981, V.16,
No.1, P.44-53 (in Russian).

13. V.G.Krotov, A note on the convergence of Fourier series in the spaces Hw, Acta Scientiarum Mathematicarum, 1979,
V.41, No.3-4, P.335-338.
http://www.math.u-szeged.hu/publikac/acta/acta.htm

12. V.G.Krotov, Unconditional convergence of Fourier series with respect to the haar system in the spaces Hw,
Matematicheskie Zametki, 1978, V.23, No.5, P.685-695 (in Russian, English transl. in Math. Notes, 1978, V.23, No.5).
http://www.springerlink.com/content/v745l267864784j4/

11. V.G.Krotov, L.Leindler, On the strong summability of Fourier series and the classes Hw, Acta Scientiarum
Mathematicarum, 1978, V. 40, No.1-2, P.93-98.
http://www.math.u-szeged.hu/publikac/acta/acta.htm

10. V.G.Krotov, Strong approximation by Fourier series and differentiability properties of functions, Analysis Mathematica,
1978, V.4, No. 3, P.199-214.
http://www.springerlink.com/content/w26k61715k2330hr/

9. V.G.Krotov, On representation of measurable functions by series in Faber-Schauder system and universal series,
Izvestija Akademii Nauk USSR, Ser. mat., 1977, V.41, No.1, P.215-229 (in Russian, English transl. in Math. USSR
Izvestija).
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=1798&option_lang=eng

8. V.G.Krotov, On the multipliers of Fourier series with respect to Haar system, Analysis Mathematica, 1977, V.3, No.3,
P.187-198.
http://www.springerlink.com/content/t6034578nm480732/

7. V.G.Krotov, P.Oswald, E.A.Storozenko, Direct and converse theorems of Jackson type in the spaces Lp, 0<p<1, Doklady
Akademii Nauk USSR, 1976, V.266, No.1, P.44-47 (in Russian, English transl. in Math. USSR Doklady).

6. V.G.Krotov, P.Oswald, E.A.Storozenko, Direct and converse theorems of Jackson type in the spaces Lp, 0<p<1,
Matematicheskij Sbornik, 1975, V.98, No.3, P.395-415 (in Russian, English transl. in Math. USSR Sbornik, 1975, V.98,
No.3).
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sm&paperid=3717&option_lang=eng
http://www.turpion.org/php/paper.phtml?journal_id=sm&paper_id=2519&year_id=1975&volume=27&issue_id=3&fpage=355&lpage=374

5. V.G.Krotov, On universal series with respect to Faber-Schauder system, Vestnik Moskovskogo universiteta, Ser.
mat.-mech. 1975, No.4, P.53-58 (in Russian).

4. V.G.Krotov, On Fourier coefficients with respect to some orthnormal system that form a basis in the space C(0,1),
Izv. Vyssh. Uchebn. Zaved. Mat. 1975, No.10, P.33-46 (in Russian, English transl. in Soviet Math. (Izv. VUZ), 1975).
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ivm&paperid=6460&option_lang=eng

3. V.G.Krotov, Continuous functions with monotone decreasing Fourier coefficients in Haar system, Sibirskiy
matematicheskiy jurnal, 1974, V.15, No.2, P.439-444(in Russian, English transl. in Siberian Math.J., 1974, V.15).
http://www.springerlink.com/content/k08l6k4430l24828/

2. V.G.Krotov, On representation of measurable functions by series in Faber-Schauder system and universal series, Doklady
Akademii Nauk SSSR, 1974, V.214, \No.6, P.1258-1261 (in Russian, English transl. in Math. USSR Doklady).

1. V.G.Krotov, On series with respect to the Faber-Schauder system and with respect to the bases of the space C[0, 1],
Matematicheskie Zametki, 1973, V.14, No.2, P.185-195 (in Russian, English transl. in Math. Notes, 1973, V.14, No.4, P.542-552).
http://www.springerlink.com/content/m264705842321617/?p=750f7477fa384ebf9f2815c5c6368603&pi=8
)