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