01.01.01 (Real analysis, complex analysis, and functional analysis)
E-mail:
Keywords:
growth spaces,
Aleksandrov-Clark measures,
pluriharmonic measures,
singular integrals,
BMO and RBMO,
tropical power series,
proper holomorphic mappings,
Uncertainty Principle,
Bloch space,
composition operators on the unit ball,
Fractional Cauchy transforms in the ball,
Ryll–Wojtaszczyk polynomials and their generalizations,
Riesz type products on the sphere,
Zygmund measures and symmetric measures.
Spaces of holomorphic and harmonic functions (one and several variables); harmonic analysis on the complex sphere; smooth measures on a sphere and on a Euclidean space.
Main publications:
Doubtsov, E., “Henkin measures, Riesz products and singular sets”, Ann. Inst. Fourier (Grenoble), 48:3 (1998), 699–728
Doubtsov, E., “Little Bloch functions, symmetric pluriharmonic measures, and Zygmunds dichotomy”, J. Funct. Anal., 170:2 (2000), 286–306
Doubtsov, E., “Differentiation properties of symmetric measures”, Potential Anal., 27:4 (2007), 389–401
Doubtsov, E., “Multipliers of fractional Cauchy transforms”, Integral Equations and Operator Theory, 64:2 (2009), 177–192
Doubtsov, E., “Carleson-Sobolev measures for weighted Bloch spaces”, J. Funct. Anal., 258:8 (2010), 2801–2816
E. Doubtsov, F. Kutzschebauch, “Factorization by elementary matrices, null-homotopy and products of exponentials for invertible matrices over rings”, Analysis and Mathematical Physics, 9:3 (2019), 1005–1018
A. B. Aleksandrov, E. Doubtsov, “Comparison of Clark Measures in Several Complex Variables”, Extended Abstracts Fall 2019, Trends in Mathematics, 12, Springer Nature, 2021, 9–16
A. B. Aleksandrov, E. Doubtsov, “Dominant Sets for Model Spaces in Several Variables”, Math. Notes, 115:2 (2024), 135–141
55.
E. Doubtsov, “Reverse Carleson measures on the closed polydisk”, Journal of Analysis, 2024, 1–11 (Published online)
56.
E. Doubtsov, “Mutual singularity of Riesz products on the unit sphere”, Proceedings of the American Mathematical Society, 2024, 1–9 (to appear)
57.
E. Doubtsov, “Compact composition operators on model spaces”, Canad. Math. Bull., 2024, 1–7 (to appear)
58.
E. Doubtsov, A. V. Vasin, “Calderón-Zygmund operators on RBMO”, Proceedings of the American Mathematical Society, 151:2 (2023), 595–610
59.
A. V. Vasin, E. Doubtsov, “A $T(P)$-Theorem for Zygmund Spaces on Domains”, Math. Notes, 114:1 (2023), 30–45
60.
E. Doubtsov, “Reverse Carleson measures for Hardy spaces in the unit ball”, Investigations on linear operators and function theory. Part 51, Zap. Nauchn. Sem. POMI, 527, POMI, St. Petersburg, 2023, 54–70
61.
E. Doubtsov, “Essential norms of weighted composition operators between Lipschitz spaces of arbitrary order”, Complex Var. Elliptic Equ., 64:4 (2019), 563–573
62.
E. Doubtsov, “Hyperbolic Hardy classes and logarithmic Bloch spaces”, Methods of Fourier Analysis and Approximation Theory, Applied and Numerical Harmonic Analysis, eds. M. Ruzhansky, S. Tikhonov, Springer, 2016, 33–42
63.
E. Doubtsov, “Integral means of weighted Hardy-Bloch functions”, Arch. Math. (Basel), 104:1 (2015), 69–76
64.
E. Doubtsov, “Radial growth of Bloch functions in the complex ball”, Arch. Math. (Basel), 102:4 (2014), 391–399
65.
E. Abakumov, E. Doubtsov, “Null-series on the complex sphere”, J. Approx. Theory, 164:10 (2012), 1427–1442
66.
E. S. Dubtsov, “Radial limits of positive solutions of the Darboux equation”, J. Math. Sci. (N.Y.), 156:5 (2009), 813–818
67.
E. Doubtsov, “Radial limits of inner functions and Bloch spaces”, Proc. Amer. Math. Soc., 136:6 (2008), 2177–2182
68.
E. S. Dubtsov, “Radial behavior of positive harmonic Bloch functions”, J. Math. Sci. (N. Y.), 148:6 (2008), 841–845
69.
E. S. Dubtsov, “Characterizations of Hardy–Orlicz and Bergman–Orlicz spaces”, J. Math. Sci. (N. Y.), 141:5 (2007), 1531–1537
70.
E. S. Dubtsov, “Bloch, Hardy, and BMOA spaces in the ball”, J. Math. Sci. (N. Y.), 139:2 (2006), 6403–6405
71.
E. S. Dubtsov, “Weakly cyclic vectors with a given modulus”, J. Math. Sci. (N. Y.), 129:4 (2005), 3990–3993
72.
E. S. Dubtsov, “Bounded cyclic functions in the ball”, J. Math. Sci. (N. Y.), 129:4 (2005), 3985–3989
73.
E. S. Dubtsov, “Regular unitarily invariant spaces on the complex sphere”, J. Math. Sci. (New York), 107:4 (2001), 4002–4021
74.
E. S. Dubtsov, “Some problems of harmonic analysis on a complex sphere”, Vestnik St. Petersburg Univ. Math., 28:1 (1995), 12–16
75.
E. S. Dubtsov, “On the radial behavior of functions holomorphic in a ball”, Vestnik St. Petersburg Univ. Math., 27:3 (1994), 21–27
Clark measures on products of spheres E. Doubtsov International Conference on Complex Analysis Dedicated to the Memory of Andrei Gonchar and Anatoliy Vitushkin October 12, 2021 17:20
Sums of moduli for holomorphic functions E. Doubtsov General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences November 19, 2012 13:00