Harmonic analysis,
complex variable methods,
theory of operators,
functional spaces,
inc. space of smooth functions,
fractional integro-differentiation,
singular,
pseudodifferential operators,
Fourier analysis.
A.N. Karapetyants, S.G. Samko, K.Zhu, “A class of Hausdorff - Berezin operators on the unit disc”, Complex Anal. Oper. Theory, 13 (2019), 3853–3870
A.N. Karapetyants, E. LIflyand, “Defining Hausdorff operators on Euclidean spaces”, Math. Meth. Appl. Sci. (2020), 1-12
A.N. Karapetyants, V.S. Rabinovich, N.L. Vasilevski, “On algebras of two dimensional singular integral operators with homogeneous discontinuities in symbols”, Integral Eq. and Oper. Theory, 40:3 (2001), 278–308
S.M. Grudsky, A.N. Karapetyants, N.L. Vasilevski, “Dynamics of properties of Toeplitz operators with radial symbols”, Integr. Equations Oper. Theory, 50 (2004), 217–253
S.M. Grudsky, A.N. Karapetyants, N.L. Vasilevski, “Dynamics of properties of Toeplitz operators on the upper half plane: Hyperbolic case”, Bol. Soc. Mat. Mexicana, 10:3 (2004), 119–138
A. N. Karapetyants, E. Berezhnoi, “A new approach to Grand and Small norms in discrete Lebesgue spaces”, Mat. Zametki (to appear)
2023
2.
Math. Notes, 114:5 (2023), 804–817
3.
Math. Notes, 114:6 (2023), 1118–1133
2022
4.
A. N. Karapetyants, I. Yu. Smirnova, “Characterization of weighted mixed norm spaces of analytic functions defined in terms of conditions on the Fourier coefficients”, Russian Math. (Iz. VUZ), 66:1 (2022), 46–52
2021
5.
A. N. Karapetyants, “On mixed norm holomorphic grand and small spaces”, Complex Variables and Elliptic Equations., 2021 (Published online)
O. Blasco, A. N. Karapetyants, J. E. Restrepo, “Boundedness of composition operators in holomorphic Holder type spaces”, Math. Meth. Appl. Sci., 2021 (to appear)
7.
A. N. Karapetyants, J. E. Restrepo., “Composition operators on holomorphic variable exponent spaces”, Math. Meth. Appl. Sci., 2021 (Published online)
A. N. Karapetyants, I. Yu. Smirnova, “Weighted holomorphic mixed norm spaces in the unit disc defined in terms of Fourier coefficients”, Complex Variables and Elliptic Equations, 2021 (Published online)
G. G. Kazaryan, A. N. Karapetyants, V. N. Margaryan, H. A. Mkrtchyan, A. G. Sergeev, “New classes of function spaces and singular operators”, Trans. Moscow Math. Soc., 82 (2021), 273–288
2020
10.
A. Karapetyants, E. Liflyand, “Defining Hausdorff operators on Euclidean spaces”, Math. Meth. Appl. Sci., 2020, 1–12
A. Karapetyants, I. Louhichi, “Fractional Integrodifferentiation and Toeplitz operators with vertical symbols”, Operator Algebras, Toeplitz Operators and Related Topics, Operator Theory: Advances and Applications, eds. W. Bauer et al. (eds.), 2020
A. Karapetyants, J. Taskinen, “Toeplitz operators with radial symbols on weighted holomorphic Orlicz space”, Operator Algebras, Toeplitz Operators and Related Topics, Operator Theory: Advances and Applications, eds. W. Bauer et al. (eds.), 2020, 189–204
A. N. Karapetyants, J. E. Restrepo, “Boundedness of projection operator and Berezin transform in generalized holomorphic and harmonic spaces of Holder type functions”, Modern Methods in Operator Theory and Harmonic Analysis, Springer Proceedings in Mathematics & Statistics, 2019, 57-66
A. N. Karapetyants, J. E. Restrepo, “Generalized Hoelder type spaces of harmonic functions in the unit ball and half space”, Czechoslovak Mathematical Journal, 2019, 1–17
A. N. Karapetyants, S. G. Samko, “On Grand and Small Bergman Spaces”, Math. Notes, 104:3 (2018), 431–436
20.
A. N. Karapetyants, S. G. Samko, “Generalized Hoelder spaces of holomorphic functions in domains in the complex plane.”, Mediterranean Journal of Mathematics, 15:226 (2018)
A. Karapetyants, H. Rafeiro, S. Samko, “Boundedness of the Bergman projection and some properties of Bergman type spaces”, Complex Analysis and Operator Theory, 2018, 1-15
A. Karapetyants, S. Samko, “Mixed norm spaces of analytic functions as spaces of generalized fractional derivatives of functions in Hardy type spaces”, Fract. Calc. Appl. Anal., 2017, no. 5, 1106-1130
A. Karapetyants, S. Samko, “On boundedness of Bergman projection operators in Banach spaces of holomorphic functions in half plane and harmonic functions in half space”, Journal of Mathematical Sciences., 226:4 (2017), 344-354
A. N. Karapetyants, S. G. Samko, “Mixed Norm Bergman–Morrey-type Spaces on the Unit Disc”, Math. Notes, 100:1 (2016), 38–48
26.
A. Karapetyants, S. Samko, “Mixed norm variable exponent Bergman space on the unit disc.”, Complex Variables and Elliptic Equations., 61:8 (2016), 1090-1106
A. N. Karapetyants, F. D. Kodzoeva, “Characterization of weighted analytic Besov spaces in terms of operators of fractional differentiation”, Fract. Calc. Appl. Anal., 17:3 (2014), 897-906
A. N. Karapetyants, F. D. Kodzoeva, “Characterization of functions from spaces defined in terms of p-integrability of mean oscillation”, Izvestya VUZOV. Severo-Kavkazskii Region. Natural Sciences, 2013, no. 6, 17-24
2012
29.
A. N. Karapetyants, I. Yu. Smirnova, “On a connection of weighted mixed norm Bergman spaces on upper half space and unit disc with Hardy spaces”, Izvestya VUZOV. Severo-Kavkazskii Region. Natural Sciences., 2012, no. 4, 15-17
30.
A. N. Karapetyants, F. D. Kodzoeva, “On certain spaces of functions defined in terms of p-integrability of mean oscillation”, Izvestya VUZOV. Severo-Kavkazskii Region. Natural Sciences., 2012, no. 4, 5-8
2010
31.
A. Karapetyants, S. Samko, “Spaces $BMO^{p(\cdot)}(\mathbb{D})$ with variable exponent $p(z)$”, Georgian Math. J., 17:3 (2010), 1572–9176
A. Karapetyants, “On functions arising as potentials with oscillating symbols”, Fractional Calc. Applied Anal., 11:4 (2008), 421-430
2006
33.
A. N. Karapetyants, V. A. Nogin, “Estimates for twisted convolution operators with singularities of kernels on a sphere and at the origin”, Differ. Equ., 42:5 (2006), 720–731
34.
A. N. Karapetyants, “The space $\mathrm{BMO}_\lambda^p(\mathbb D)$, compact Toeplitz operators with $\mathrm{BMO}_\lambda^1(\mathbb D)$ symbols on weighted Bergman spaces, and the Berezin transform”, Russian Math. (Iz. VUZ), 50:8 (2006), 71–74
35.
A. N. Karapetyants, V. A. Nogin, “$L_p\to L_q$-estimates for a twisted convolution operator with a kernel that has singularities on a sphere and at the origin”, Russian Math. (Iz. VUZ), 50:2 (2006), 67–72
36.
N. L. Vasilevskii, S. M. Grudskii, A. N. Karapetyants, “Dynamics of properties of Toeplitz operators on weighted Bergman spaces”, Sib. Èlektron. Mat. Izv., 3 (2006), 362–383
37.
A. N. Karapetyants, “Toeplitz operators with radial symbols on weighted Bergman spaces on the unit disc”, Vestnik of Southern Scientific Center of Russian Academy of Sciences, 2:1 (2006), 3-9
38.
A. N. Karapetyants, “On functions represented as potential with oscillating at infinity symbol”, Izvestya VUZOV. Severo-Kavkazskii Region. Natural Sciences, 2006, no. 7, 22–33
39.
A. N. Karapetyants, V. A. Nogin, “Estimates for twisted convolution operators with singularities of kernels on a sphere and at the origin”, Differential Equations, 42:5 (2006), 720–731
A. N. Karapetyants, “Characterization of weighted $BMO^1_\lambda(\mathbb D)$ spaces in terms of mean oscillation in the Bergman metric”, Izvestya VUZOV. Severo-Kavkazskii Region. Natural Sciences, 2006, no. 1, 15–19
41.
A. N. Karapetyants, F. D. Kodzoeva, “Characterization of functions from analytic weighted Besov space on a unit disc.”, Complex analysis. The theory of operators. Mathematical modeling., eds. Yu. F. Korobeinik and A. G. Kusrayev, Vladikavkaz: Vladikavkaz Scientific Center of Russian Academy of Sciences, 2006, 48–62
42.
A. N. Karapetyants, V. A. Nogin, “$L_p \to L_q$ - estimates for the twisted convolution operators whose kernel has singularities on a sphere and at the origin of coordinates”, Russian Mathematics (Iz. VUZ), 50:2 (2006), 69–72
2005
43.
A. N. Karapetyants, A. V. Golikov, “The Berezin transform and radial operators in weighted Bergman spaces in the unit disk”, Vladikavkaz. Mat. Zh., 7:2 (2005), 55–63
44.
A. N. Karapetyants, F. D. Kodzoeva, “Analytic weighted Besov spaces on the unit disk”, Proc. A.Razmadze Math. Inst., 139 (2005), 125–127
45.
A. N. Karapetyants, “Toeplitz operators with BMO symbols on weighted Bergman spaces and Berezin transform”, Izvestya VUZOV. Severo-Kavkazskii Region. Natural Sciences., 2005, Special Issue: Pseudo-differential equations and some problems of mathematical physics, 78–82
46.
A. N. Karapetyants, “Characterization of functions from weighted $BMO^1_\lambda(\mathbb D)$ space over unit disc.”, Izvestya VUZOV. Severo-Kavkazskii Region, 2005, no. 9, 8–17
47.
A. N. Karapetyants, A. V. Golikov, “Berezin transform and radial operators on weighted Bergman space on the unit disc”, Vladikavkaz Math. Journal, 7:2 (2005), 55–63
A. N. Karapetyants, D. N. Karasev, V. A. Nogin, “$L_p \to L_q$-estimates for the fractional acoustic potentials and some related operators”, Fract. Calc. Appl. Anal., 8:2 (2005), 155–172
2004
49.
S. M. Grudsky, A. N. Karapetyants, N. L. Vasilevski, “Dynamics of properties of Toeplitz operators on the upper half plane: Parabolic case”, J. Operator Theory, 52:1 (2004), 185–214
50.
S. M. Grudsky, A. N. Karapetyants, N. L. Vasilevski, “Dynamics of properties of Toeplitz operators on the upper half plane: Hyperbolic case”, Bol. Soc. Mat. Mexicana, 10:2 (2004), 119–138
51.
S. M. Grudsky, A. N. Karapetyants, N. L. Vasilevski, “Dynamics of properties of Toeplitz operators with radial symbols”, Integral Equations Operator Theory, 50:2 (2004), 217-253
A. N. Karapetyants, D. N. Karasev, V. A. Nogin, “Estimates for some potential type operators with oscillating kernels”, in J. Contemp. Math. Anal., 38:2 (2003), 35-61
53.
A. N. Karapetyants, E. Ramirez de Arellano, “$L_p \to L_q$ boundedness for some convolution and twisted convolution operators”, Singular Integral Operators, Factorization and Applications Proceedings, Operator Theory: Advances and Applications, Birkauser Verlag, 2003, 133-145
54.
S. M. Grudsky, A. N. Karapetyants, N. L. Vasilevski, “Toeplitz operators on the unit ball in $\mathbb{C}^n$ with radial symbols,”, J. Operator Theory, 49:2 (2003), 325–346
55.
A. N. Karapetyants, E Ramirez de Arellano, “A boundedness result for twisted convolution”, Math. Nachr., 250 (2003), 58–70
A. N. Karapetyants, V. A. Nogin, “Complex powers of the second order non-homogeneous elliptic differential operators with degenerating symbols in the spaces $L_p(\mathbb{R}^n)$”, Bol. Soc. Mat. Mexicana, 7:3 (2001), 193–209
57.
A. N. Karapetyants, V. S. Rabinovich, N. L. Vasilevski, “On algebras of two dimensional singular integral operators with homogeneous discontinuities in symbols”, Integral Equations Operator Theory, 40:3 (2001), 278–308
A. N. Karapetyants, V. A. Nogin, “On $L$ characteristic of some potential type operators with oscillating symbols and singularities of the kernels on a sphere”, Acta Mathematica Hungarica, 92:1–2 (2001), 1–10
A. N. Karapetyants, E. Ramirez de Arellano, “On the inversion of potential type operators with kernels having singularities on a sphere”, Fractional Calculus and Applied Analysis, 3:2 (2000), 141–160
61.
A. N. Karapetyants, V. A. Nogin, “On the $L$-characteristic of some potential-type operators with oscillating symbols and singularities of the kernels on a sphere”, Dokl. Akad. Nauk, 370:3 (2000), 300–302
1999
62.
A. N. Karapetyants, V. A. Nogin, “Inversion of potential-type operators with kernels possessing singularities on the sphere”, Izv. Nats. Akad. Nauk Armenii. Math., 34:1 (1999), 57–71
63.
A. N. Karapetyants, E. Ramirez de Arellano, “Characterization of anisotropic Lizorkin-type mixed norm spaces generated by degenerate differential operators”, Fract. Calc. Appl. Anal., 2:2 (1999), 193–204
1998
64.
A. N. Karapetyants, V. A. Nogin, “Characterization of functions in anisotropic spaces of complex order”, Russian Math. (Iz. VUZ), 42:5 (1998), 22–28
65.
A. N. Karapetyants, V. A. Nogin, “Characterization of functions in anisotropic spaces of complex order”, Izv. Vyssh. Uchebn. Zaved. Mat., 1998, no. 5, 24–30
66.
A. N. Karapetyants, V. A. Nogin, “Complex powers of second order elliptic differential operators with degenerating symbols in the spaces $L_p(\mathbb{R}^n)$,”, Dokl. Akad. Nauk, 358:1 (1998), 10–12
1996
67.
A. N. Karapetyants, V. A. Nogin, “Inversion of some multiplicative operators in the spaces $L_p(\mathbb{R}^n)$”, Boundary value problems, special functions and fractional calculus., 1996, 98–100
68.
A. N. Karapetyants, V. A. Nogin, “The description of functions in anisotropic spaces of complex order and its application”, Dokl. Akad. Nauk, 351:1 (1996), 13–15
Presentations in Math-Net.Ru
1.
Aggrandization of spaces of holomorphic functions A. N. Karapetyants International Scientific Conference
“Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis - 2024”
(OTHA-2024) August 26, 2024 11:45
On a class of Hadamard-Bergman operators S. M. Grudskii, A. N. Karapetyants, A. R. Mirotin VI International Conference "Function Spaces. Differential Operators. Problems of Mathematical Education", dedicated to the centennial anniversary of the corresponding member of Russian Academy of Sciences, academician of European Academy of Sciences L.D. Kudryavtsev November 16, 2023 10:55
Hausdorff-Berezin operators on weighted spaces A. N. Karapetyants International scientific workshop OTHA Spring 2023 on operator theory and harmonic analysis and their applications April 19, 2023 11:55
2023
Contact us: