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Lizorkin, Petr Ivanovich
(1922–1993)

Statistics Math-Net.Ru
Total publications: 83
Scientific articles: 74

Number of views:
This page:1324
Abstract pages:14552
Full texts:6692
References:204
Professor
Doctor of physico-mathematical sciences (1969)
Birth date: 03.04.1922

http://www.mathnet.ru/eng/person20378
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/114985

Publications in Math-Net.Ru
1995
1. V. S. Guliev, P. I. Lizorkin, “Spaces of Banach-valued analytic and periodic functions”, Trudy Mat. Inst. Steklov., 210 (1995),  101–119  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 210 (1995), 74–88
1993
2. P. I. Lizorkin, Kh. P. Rustamov, “Nikol'skij–Besov spaces on the sphere in connection with approximation theory”, Trudy Mat. Inst. Steklov., 204 (1993),  172–200  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 204 (1994), 149–172
3. V. S. Guliev, P. I. Lizorkin, “Classes of holomorphic and harmonic functions in the polydisk in connection with their boundary values”, Trudy Mat. Inst. Steklov., 204 (1993),  137–159  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 204 (1994), 117–135
1992
4. P. I. Lizorkin, V. S. Guliev, “Functional spaces and approximation problems on Heisenberg group”, Trudy Mat. Inst. Steklov., 201 (1992),  245–272  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 201 (1994), 205–227
5. P. I. Lizorkin, “Direct and inverse theorems of approximation theory for functions on Lobachevsky space”, Trudy Mat. Inst. Steklov., 194 (1992),  120–147  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 194 (1993), 125–151
1991
6. P. I. Lizorkin, “Approximation on Riemannian manifold”, Trudy Mat. Inst. Steklov., 200 (1991),  222–235  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 200 (1993), 247–260
1990
7. P. I. Lizorkin, “Classes of functions constructed on the basis of averages over spheres. (The case of spaces of Sobolev type)”, Trudy Mat. Inst. Steklov., 192 (1990),  122–139  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 192 (1992), 131–149
1989
8. K. Kh. Boimatov, P. I. Lizorkin, “Estimates for the growth of solutions of differential equations”, Differ. Uravn., 25:4 (1989),  578–588  mathnet  mathscinet; Differ. Equ., 25:4 (1989), 386–393
9. P. I. Lizorkin, V. B. Shakhmurov, “Embedding theorems for vector-valued functions. II”, Izv. Vyssh. Uchebn. Zaved. Mat., 1989, 2,  47–54  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 33:2 (1989), 53–61
10. P. I. Lizorkin, V. B. Shakhmurov, “Embedding theorems for vector-valued functions. I”, Izv. Vyssh. Uchebn. Zaved. Mat., 1989, 1,  70–79  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 33:1 (1989), 81–90
11. P. I. Lizorkin, S. M. Nikol'skii, “Functional spaces of mixed smoothness from decompositional point of view”, Trudy Mat. Inst. Steklov., 187 (1989),  143–161  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 187 (1990), 163–184
12. K. S. Kazarian, P. I. Lizorkin, “Multiplicators, basises, unconditional basises in weighted spaces В and SB”, Trudy Mat. Inst. Steklov., 187 (1989),  98–115  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 187 (1990), 111–130
1988
13. P. I. Lizorkin, N. V. Miroshin, “The generalized Poisson integral and the smoothness of the solution of the Dirichlet problem for degenerate elliptic operators”, Differ. Uravn., 24:2 (1988),  305–313  mathnet  mathscinet; Differ. Equ., 24:2 (1988), 232–239
14. S. M. Nikol'skiĭ, P. I. Lizorkin, N. V. Miroshin, “Weighted function spaces and their applications to the investigation of boundary value problems for degenerate elliptic equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 1988, 8,  4–30  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 32:8 (1988), 1–40
15. O. V. Besov, L. D. Kudryavtsev, P. I. Lizorkin, S. M. Nikol'skii, “Investigations in the theory of spaces of differentiable functions of several variables”, Trudy Mat. Inst. Steklov., 182 (1988),  68–127  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 182 (1990), 73–139
16. S. M. Nikol'skii, P. I. Lizorkin, “A new approach to the theory of function spaces $B^r_{p,\theta}$ on a sphere”, Trudy Mat. Inst. Steklov., 181 (1988),  213–221  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 181 (1989), 233–242
1987
17. S. M. Nikol'skii, P. I. Lizorkin, “Approximation of functions on the sphere”, Izv. Akad. Nauk SSSR Ser. Mat., 51:3 (1987),  635–651  mathnet  mathscinet  zmath; Math. USSR-Izv., 30:3 (1988), 599–614
18. S. M. Nikol'skii, P. I. Lizorkin, “Functional spaces on the sphere, related with approximation theory”, Mat. Zametki, 41:4 (1987),  509–516  mathnet  mathscinet  zmath; Math. Notes, 41:4 (1987), 286–291  isi
1986
19. S. M. Nikol'skii, P. I. Lizorkin, “Inequalities for harmonic, spherical and algebraic polynomials”, Dokl. Akad. Nauk SSSR, 289:3 (1986),  541–545  mathnet  mathscinet  zmath
20. S. M. Nikol'skii, P. I. Lizorkin, “Approximation of functions by spherical polynomials in the metric $L_p$”, Dokl. Akad. Nauk SSSR, 289:2 (1986),  285–289  mathnet  mathscinet  zmath
21. S. M. Nikol'skii, P. I. Lizorkin, “Inequalities of Bernstein type for spherical polynomials”, Dokl. Akad. Nauk SSSR, 288:1 (1986),  50–53  mathnet  mathscinet  zmath
22. V. A. Ivanov, P. I. Lizorkin, “Estimates in integral norms of derivatives of harmonic polynomials and spherical polynomials”, Dokl. Akad. Nauk SSSR, 286:1 (1986),  23–27  mathnet  mathscinet  zmath
23. P. I. Lizorkin, N. V. Miroshin, “Smoothness of the solution of the first boundary value problem for a second-order model degenerate elliptic differential operator”, Differ. Uravn., 22:11 (1986),  1945–1951  mathnet  mathscinet
24. P. I. Lizorkin, S. M. Nikol'skii, “Approximation by spherical functions”, Trudy Mat. Inst. Steklov., 173 (1986),  181–189  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 173 (1987), 195–203
25. P. I. Lizorkin, “Limit cases of theorems on $\mathscr F L_p$-multipliers”, Trudy Mat. Inst. Steklov., 173 (1986),  164–180  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 173 (1987), 177–194
26. P. I. Lizorkin, “On the theory of Fourier multipliers”, Trudy Mat. Inst. Steklov., 173 (1986),  149–163  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 173 (1987), 161–176
1985
27. S. M. Nikol'skii, P. I. Lizorkin, “Approximation theory on the sphere”, Trudy Mat. Inst. Steklov., 172 (1985),  272–279  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 172 (1987), 295–302
28. P. I. Lizorkin, “On the theory of degenerate elliptic equations”, Trudy Mat. Inst. Steklov., 172 (1985),  235–251  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 172 (1987), 257–274
1984
29. P. I. Lizorkin, M. O. Otelbaev, “Estimates of approximate numbers of the imbedding operators for spaces of Sobolev type with weights”, Trudy Mat. Inst. Steklov., 170 (1984),  213–232  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 170 (1987), 245–266
30. S. M. Nikol'skii, P. I. Lizorkin, “Approximation by spherical polynomials”, Trudy Mat. Inst. Steklov., 166 (1984),  186–200  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 166 (1986), 207–222
1983
31. P. I. Lizorkin, S. M. Nikol'skii, “Approximation on a sphere in the metric of the continuous functions”, Dokl. Akad. Nauk SSSR, 272:3 (1983),  524–528  mathnet  mathscinet  zmath
32. P. I. Lizorkin, S. M. Nikol'skii, “Approximation on the sphere in $L_2$”, Dokl. Akad. Nauk SSSR, 271:5 (1983),  1059–1063  mathnet  mathscinet  zmath
33. P. I. Lizorkin, S. M. Nikol'skii, “Coercive properties of an elliptic equation with degeneration and a generalized right-hand side”, Trudy Mat. Inst. Steklov., 161 (1983),  157–183  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 161 (1984), 171–198
1981
34. P. I. Lizorkin, S. M. Nikol'skii, “Coercive properties of an elliptic equation with degeneracy”, Dokl. Akad. Nauk SSSR, 259:1 (1981),  28–30  mathnet  mathscinet  zmath
35. P. I. Lizorkin, S. M. Nikol'skii, “Elliptic equations with degeneracy. Differential properties of solutions”, Dokl. Akad. Nauk SSSR, 257:2 (1981),  278–282  mathnet  mathscinet  zmath
36. P. I. Lizorkin, S. M. Nikol'skii, “An elliptic equation with degeneracy. A variational method”, Dokl. Akad. Nauk SSSR, 257:1 (1981),  42–45  mathnet  mathscinet  zmath
37. P. I. Lizorkin, S. M. Nikol'skii, “Coercive properties of elliptic equations with degeneration. Variational method”, Trudy Mat. Inst. Steklov., 157 (1981),  90–118  mathnet  mathscinet  zmath
1980
38. P. I. Lizorkin, M. Otelbaev, “Imbedding theorems and compactness for spaces of Sobolev type with weights. II”, Mat. Sb. (N.S.), 112(154):1(5) (1980),  56–85  mathnet  mathscinet  zmath; Math. USSR-Sb., 40:1 (1981), 51–77  isi
39. P. I. Lizorkin, “Estimate of mixed and intermediate derivatives in weighted $L_p$-norms”, Trudy Mat. Inst. Steklov., 156 (1980),  130–142  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 156 (1983), 141–153
1979
40. P. I. Lizorkin, M. Otelbaev, “Imbedding theorems and compactness for spaces of Sobolev type with weights”, Mat. Sb. (N.S.), 108(150):3 (1979),  358–377  mathnet  mathscinet  zmath; Math. USSR-Sb., 36:3 (1980), 331–349  isi
41. P. I. Lizorkin, “Behavior at infinity of functions from Liouville classes. Riesz potentials of arbitrary order”, Trudy Mat. Inst. Steklov., 150 (1979),  174–197  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 150 (1981), 185–209
1978
42. P. I. Lizorkin, “On the closure of the set of compactly supported functions in the weighted space $W^l_{p,\Phi}$”, Dokl. Akad. Nauk SSSR, 239:4 (1978),  789–792  mathnet  mathscinet  zmath
1977
43. P. I. Lizorkin, “Bases and multipliers in the spaces $B^r_{p,\theta }(\Pi)$”, Trudy Mat. Inst. Steklov., 143 (1977),  88–104  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 143 (1980), 93–110
1976
44. P. I. Lizorkin, “Interpolation of $L_p$ spaces with weight”, Trudy Mat. Inst. Steklov., 140 (1976),  201–211  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 140 (1979), 221–232
1975
45. P. I. Lizorkin, “Interpolation of weighted $L_p$-spaces”, Dokl. Akad. Nauk SSSR, 222:1 (1975),  32–35  mathnet  mathscinet  zmath
46. P. I. Lizorkin, “The functional characterization of the interpolation spaces $(L_p(\Omega),W^1_p(\Omega))_{\theta,p}$”, Trudy Mat. Inst. Steklov., 134 (1975),  180–203  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 134 (1977), 203–227
1974
47. P. I. Lizorkin, “Properties of functions in the spaces $\Lambda ^r_{p,\theta }$”, Trudy Mat. Inst. Steklov., 131 (1974),  158–181  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 131 (1974), 165–188
1972
48. P. I. Lizorkin, “On a theorem of Marcinkiewicz type for $H$-valued functions. A continual form of the Paley–Littlewood theorem”, Mat. Sb. (N.S.), 87(129):2 (1972),  229–235  mathnet  mathscinet  zmath; Math. USSR-Sb., 16:2 (1972), 237–243
49. P. I. Lizorkin, “Generalized Hölder classes of functions in connection with fractional differentiation”, Trudy Mat. Inst. Steklov., 128 (1972),  172–177  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 128 (1972), 203–209
50. P. I. Lizorkin, “Operators connected with fractional differentiation, and classes of differentiable functions”, Trudy Mat. Inst. Steklov., 117 (1972),  212–243  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 117 (1972), 251–286
1970
51. P. I. Lizorkin, “Multipliers of Fourier integrals and bounds of convolution in spaces with mixed norms. Applications”, Izv. Akad. Nauk SSSR Ser. Mat., 34:1 (1970),  218–247  mathnet  mathscinet  zmath; Math. USSR-Izv., 4:1 (1970), 225–255
52. P. I. Lizorkin, “Description of the spaces $L_p^r(R^n)$ in terms of singular difference integrals”, Mat. Sb. (N.S.), 81(123):1 (1970),  79–91  mathnet  mathscinet  zmath; Math. USSR-Sb., 10:1 (1970), 77–89
1969
53. P. I. Lizorkin, S. M. Nikol'skii, “Compactness of sets of differentiable functions”, Trudy Mat. Inst. Steklov., 105 (1969),  168–177  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 105 (1969), 203–215
54. P. I. Lizorkin, “Generalized Liouville differentiation and the multiplier method in the theory of imbeddings of classes of differentiable functions”, Trudy Mat. Inst. Steklov., 105 (1969),  89–167  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 105 (1969), 105–202
1968
55. P. I. Lizorkin, “Generalized Liouville differentiation and the method of multiplicators in imbedding theory for function classes”, Mat. Zametki, 4:4 (1968),  467–482  mathnet  mathscinet; Math. Notes, 4:4 (1968), 771–779
1967
56. O. V. Besov, P. I. Lizorkin, “Singular integral operators and sequences of convolutions in $L_p$ spaces”, Mat. Sb. (N.S.), 73(115):1 (1967),  65–88  mathnet  mathscinet  zmath; Math. USSR-Sb., 2:1 (1967), 57–76
57. P. I. Lizorkin, “On multipliers of Fourier integrals in the spaces $L_{p,\theta}$”, Trudy Mat. Inst. Steklov., 89 (1967),  231–248  mathnet  mathscinet  zmath
58. P. I. Lizorkin, “Theorems of Littlewood–Paley type for multiple Fourier integrals”, Trudy Mat. Inst. Steklov., 89 (1967),  214–230  mathnet  mathscinet  zmath
1966
59. P. I. Lizorkin, “Nonisotropic Bessel potentials. Imbedding theorems for the Sobolev space $L_p^{(r_1,…,r_n)}$ with fractional derivatives”, Dokl. Akad. Nauk SSSR, 170:3 (1966),  508–511  mathnet  mathscinet  zmath
60. O. V. Besov, V. P. Il'in, P. I. Lizorkin, “The $L_p$-estimates of a certain class of non-isotropically singular integrals”, Dokl. Akad. Nauk SSSR, 169:6 (1966),  1250–1253  mathnet  mathscinet  zmath
1965
61. P. I. Lizorkin, “Fourier transformation in Besov spaces. The zero scale of $B^0_{p,\theta}$”, Dokl. Akad. Nauk SSSR, 163:6 (1965),  1318–1321  mathnet  mathscinet  zmath
62. P. I. Lizorkin, “Bounds for trigonometrical integrals and an inequality of Bernstein for fractional derivatives”, Izv. Akad. Nauk SSSR Ser. Mat., 29:1 (1965),  109–126  mathnet  mathscinet  zmath
63. P. I. Lizorkin, S. M. Nikol'skii, “Classification of differentiable functions on the basis of spaces with dominant mixed derivatives”, Trudy Mat. Inst. Steklov., 77 (1965),  143–167  mathnet  mathscinet  zmath
1964
64. S. M. Nikol'skii, P. I. Lizorkin, “Some inequalities for functions of weight classes and boundary-value problems with strong degeneracy on the boundary”, Dokl. Akad. Nauk SSSR, 159:3 (1964),  512–515  mathnet  mathscinet  zmath
65. P. I. Lizorkin, “Functions of Hirschman type and relations between the spaces $B_p^r(E_n)$ and $L_p^r(E_n)$”, Mat. Sb. (N.S.), 63(105):4 (1964),  505–535  mathnet  mathscinet  zmath
1963
66. P. I. Lizorkin, “$(L_p,L_q)$-multipliers of Fourier integrals”, Dokl. Akad. Nauk SSSR, 152:4 (1963),  808–811  mathnet  mathscinet  zmath
67. P. I. Lizorkin, “Characteristics of boundary values of functions of $L^r_p(E_n)$ on hyperplanes”, Dokl. Akad. Nauk SSSR, 150:5 (1963),  984–986  mathnet  mathscinet  zmath
68. P. I. Lizorkin, “Generalized Liouville differentiation and the functional spaces $L_p^r(E_n)$. Imbedding theorems”, Mat. Sb. (N.S.), 60(102):3 (1963),  325–353  mathnet  mathscinet  zmath
1962
69. P. I. Lizorkin, “$L_p^r(\Omega)$ spaces. Continuation and imbedding theorems”, Dokl. Akad. Nauk SSSR, 145:3 (1962),  527–530  mathnet  mathscinet  zmath
70. P. I. Lizorkin, “Imbedding theorems for functions of $L_p^r$”, Dokl. Akad. Nauk SSSR, 143:5 (1962),  1042–1045  mathnet  mathscinet  zmath
1961
71. P. I. Lizorkin, “The Green's $E$-function of a Beltrami operator and some variational problems”, Dokl. Akad. Nauk SSSR, 139:5 (1961),  1052–1055  mathnet  mathscinet  zmath
72. A. A. Vasharin, P. I. Lizorkin, “Certain boundary-value problems for elliptic equations with strong degeneration at the boundary”, Dokl. Akad. Nauk SSSR, 137:5 (1961),  1015–1018  mathnet  mathscinet  zmath
1960
73. P. I. Lizorkin, “The Dirichlet principle for the Beltrami equation in a semi-space”, Dokl. Akad. Nauk SSSR, 134:4 (1960),  761–764  mathnet  mathscinet  zmath
74. P. I. Lizorkin, “Boundary properties of functions from “weight” classes”, Dokl. Akad. Nauk SSSR, 132:3 (1960),  514–517  mathnet  mathscinet  zmath

1993
75. O. V. Besov, V. A. Il'in, P. I. Lizorkin, S. M. Nikol'skii, S. I. Pokhozhaev, T. S. Pigolkina, “Lev Dmitrievich Kudryavtsev (on his seventieth birthday)”, Uspekhi Mat. Nauk, 48:4(292) (1993),  242–244  mathnet  mathscinet; Russian Math. Surveys, 48:4 (1993), 261–165  isi
1992
76. O. V. Besov, E. A. Volkov, V. K. Dzyadyk, N. P. Korneichuk, L. D. Kudryavtsev, P. I. Lizorkin, “Sergei Mikhailovich Nikol'skii (On occasion of eighty fifth birthday)”, Trudy Mat. Inst. Steklov., 201 (1992),  3–13  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 201 (1994), 1–9
1984
77. V. A. Il'in, L. D. Kudryavtsev, P. I. Lizorkin, S. M. Nikol'skii, A. A. Samarskii, A. N. Tikhonov, “Ivan Aleksandrovich Kipriyanov (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 39:2(236) (1984),  213–214  mathnet  mathscinet; Russian Math. Surveys, 39:2 (1984), 219–221  isi
1983
78. S. M. Nikol'skii, O. V. Besov, P. I. Lizorkin, “Lev Dmitrievich Kudryavtsev (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 38:3(231) (1983),  205–210  mathnet  mathscinet  zmath; Russian Math. Surveys, 38:3 (1983), 179–185  isi
1978
79. P. I. Lizorkin, “Intgegral transformations of generalized functions: Yu. A. Brychkov and A. P. Prudnikov. 286 p. “Nauka”, Moscow, 1977. Book review”, Zh. Vychisl. Mat. Mat. Fiz., 18:4 (1978),  1063–1064  mathnet; U.S.S.R. Comput. Math. Math. Phys., 18:4 (1978), 251–252
1977
80. K. A. Bezhanov, O. V. Besov, A. V. Bitsadze, I. A. Borachinsky, A. A. Vasharin, V. S. Vladimirov, N. V. Zvolinsky, V. A. Il'in, V. P. Korobeinikov, L. D. Kudryavtsev, L. P. Kuptsov, P. I. Lizorkin, Yu. I. Makarychev, V. E. Mirakov, V. P. Mikhailov, E. F. Mishchenko, S. M. Nikol'skii, Yu. S. Nikol'skii, A. P. Novikov, T. S. Pigolkina, S. I. Pokhozhaev, E. A. Romishevsky, S. L. Sobolev, S. V. Uspenskii, M. I. Shabunin, G. N. Yakovlev, “Владимир Михайлович Шалов (некролог)”, Differ. Uravn., 13:6 (1977),  1149–1153  mathnet
81. P. I. Lizorkin, S. M. Nikol'skii, S. L. Sobolev, S. V. Uspenskii, “The Fifth Soviet–Czechoslovak Meeting on Applications of Methods of Function Theory and Functional Analysis for Problems of Mathematical Physics”, Uspekhi Mat. Nauk, 32:3(195) (1977),  217–225  mathnet
1972
82. L. D. Kudryavtsev, P. I. Lizorkin, S. M. Nikol'skii, S. L. Sobolev, “Vladimir Iosifovich Kondrashov (obituary)”, Uspekhi Mat. Nauk, 27:2(164) (1972),  149–155  mathnet  mathscinet  zmath; Russian Math. Surveys, 27:2 (1972), 83–90
1963
83. P. I. Lizorkin, “Methods of Mathematical Physics, Vol. 2. Partial Differential Equations. Book Review”, Zh. Vychisl. Mat. Mat. Fiz., 3:2 (1963),  411–412  mathnet; U.S.S.R. Comput. Math. Math. Phys., 3:2 (1963), 548–550

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