Karen Avetisyan 's Publications (Full profile)
Paper
- , Estimates for harmonic reproducing kernel and Bergman type operators on mixed norm and Besov spaces in the real ball, Annals of Functional Analysis, 14, (2, Article 40), pp. 29 pages, (2023)
- , Marcinkiewicz--Zygmund type inequalities in the real ball, Journal of Contemporary Mathematical Analysis, 57, (1), pp. 35-42, (2022)
- , Fractional integration in weighted Lebesgue spaces, Journal of Contemporary Mathematical Analysis, 56, (2), pp. 57--67, (2021)
- , Poisson-Bergman type operators on Lipschitz and mixed norm spaces in the real ball, Lobachevskii J. Math., 40, (8), pp. 1025-1033, (2019)
- , On weighted Dirichlet spaces of monogenic functions in R^3, Mathematical Methods in the Applied Sciences, 41, (18), pp. 9511-9528, (2018)
- , Normal weighted Bergman type operators on mixed norm spaces over the ball in C^n, J. Korean Math. Soc. , 55, (2), pp. 313–326, (2018)
- , Weighted spaces of harmonic functions in the unit ball, Proc. Yerevan State Univ., Phys. Math. Sci. , 51, (1), pp. 3-7, (2017)
- , On some Bergman type operators with normal weights over the ball in C^n [in Russian] , Dokl. Nat. Akad. Nauk Armenii, 116, (4), pp. 270-277, (2016)
- , Bergman type operators on mixed norm spaces over the ball in C^n , Izvestiya NAN Armenii, Matematika, 51, (5), pp. 3-12 , (2016)
- , On the fractional integro-differentiation operator in R^n, Izvestiya NAN Armenii, Matematika , 50, (5), pp. 3-16 , (2015)
- , Subharmonicity and a version of Riesz theorem on harmonic conjugates, Advances in Applied Clifford Algebras, 24 , (4 ), pp. 909--919, (2014)
- , Sharp inclusions and lacunary series in mixed norm spaces on the polydisc, Complex Variables and Elliptic Equations, 58, (2), pp. 185-195, (2013)
- , On Riesz systems of harmonic conjugates in R^3, Mathematical Methods in the Applied Sciences, 36, (12), pp. 1598-1614, (2013)
- , Continuous embeddings in harmonic mixed norm spaces on the unit ball in R^n, Izvestiya NAN Armenii, Matematika, 47, (5), pp. 3-20, (2012)
- , A note on mixed norm spaces of analytic functions, Australian J. Math. Anal. Appl., 9, (1, Article 16), pp. 1-6, (2012)
- , Lacunary series in mixed norm spaces in the disc [in Russian], Izvestiya NAN Armenii, Matematika, 45, (5), pp. 9-18, (2010)
- , Weighted spaces of harmonic and holomorphic functions
[in Russian], Dc.Sc. Doctoral Thesis,
, Armenian J. Math., 2, (4), pp. 225 pages, (2009)
- , Holomorphic functions on the mixed norm spaces on the polydisc (II) , J. Comput. Analysis Appl., 11, ( 2), pp. 239-251, (2009)
- , Extended Cesaro operators between different Hardy spaces, Appl. Math. Comput. , 207, (2), pp. 346-350, (2009)
- , The generalized Libera transform is bounded on the Besov mixed-norm, BMOA and VMOA spaces on the unit disc, Appl. Math. Comput., 213, (2), pp. 304-311, (2009)
- , Harmonic conjugates in weighted Bergman spaces of quaternion-valued functions, Comput. Methods Funct. Theory , 9, (2), pp. 593-608, (2009)
- , Weighted integrals and Bloch spaces of n-harmonic functions on the polydisc, Potential Analysis, 29, (1), pp. 49-63, (2008)
- , Lacunary series and sharp estimates in weighted spaces of holomorphic functions. [in Russian] , Izvestiya NAN Armenii, Matematika, 42, (2), pp. 3-9, (2007)
- , Hardy-Stein identities and Littlewood-Paley inequalities
in polydisc [in Russian]
, Izvestiya NAN Armenii, Matematika, 42, (3), pp. 3-13, (2007)
- , Equivalent conditions for Bergman space and Littlewood-Paley type inequalities, J. Comput. Analysis Appl., 9, (1), pp. 15-28, (2007)
- , Littlewood-Paley inequalities in uniformly convex and uniformly smooth Banach spaces, J. Math. Anal. Appl., 336, (1), pp. 31-43, (2007)
- , Hardy-Bloch type spaces and lacunary series on the polydisk , Glasgow Math. J. , 49, (2), pp. 345-356, (2007)
- , Some generalizations of Littlewood-Paley inequality in the polydisc, Mat. Vesnik, 58, (3-4), pp. 97-110, (2006)
- , Integral representations in general weighted Bergman spaces, Complex Variables Theory Appl. , 50, (15), pp. 1151-1161, (2005)
- , Generalized problem of Littlewood, [in Russian], Izv. Nat. Akad. Nauk Armenii, Matematika, 40, (3), pp. 3-15, (2005)
- , Inequalities of Littlewood-Paley type for n-harmonic functions on the polydisk, [in Russian], Mat. Zametki, 75, (4), pp. 483-492, (2004)
- , Continuous inclusions and Bergman type operators in n-harmonic mixed norm spaces on the polydisc, J. Math. Anal. Appl. , 291, (2), pp. 727-740, (2004)
- , Bergman type projection in the Besov spaces, [in Russian], Izv. Nat. Akad. Nauk Armenii, Matematika, 38, (6), pp. 5-16, (2003)
- , On fractional integro-differentiation in harmonic mixed norm classes on a half-space, [in Russian], Dokl. Nat. Akad. Nauk Armenii, 102, (1), pp. 5-10, (2002)
- , On a general theory of classes of regular functions weighted area-integrable on a disk, [in Russian], Dokl. Nat. Akad. Nauk Armenii, 102, (2), pp. 105-112, (2002)
- , On Littlewood-Paley type inequalities, [in Russian], Dokl. Nat. Akad. Nauk Armenii, 101, (1), pp. 20-23, (2001)
- , Bounded projections on harmonic mixed norm spaces, [in Russian], Dokl. Nat. Akad. Nauk Armenii, 101, (3), pp. 211-215, (2001)
- , Littlewood-Paley type inequalities for $R^n$ [in Russian] , Izv. Nat. Akad. Nauk Armenii, Matematika, 36, (3), pp. 5-11, (2001)
- , Fractional integro-differentiation in harmonic mixed norm spaces on a half-space, Comment. Math. Univ. Carolinae, 42, (4), pp. 691-709, (2001)
- , Fractional integration and integral representations in weighted classes of harmonic functions, Analysis Mathematica, 26, (3), pp. 161-174, (2000)
- , On fractional integration and integral representations in classes of harmonic functions on the disk, [in Russian], Dokl. Nat. Akad. Nauk Armenii, 99, (4), pp. 301-305, (1999)
- , Green type potentials and representability of some weighted classes of subharmonic functions, [in Russian], Izv. Nat. Akad. Nauk Armenii, Matematika, 30, (2), pp. 3-34, (1995)
- , On representation of some classes of functions subharmonic in the unit disk and in the half-plane, [in Russian], Izv. Nat. Akad. Nauk Armenii, Matematika, 29, (1), pp. 3-15, (1994)
Book
- , Local and constrained extrema [in Armenian], Yerevan State Univ. Press, pp. 132, (2018)
- , Asymptotic methods [in Armenian] , Yerevan State Univ. Press, pp. 120, (2007)
Conference Paper
- , On normal weighted Bergman type operators on mixed norm spaces , Armenian Mathematical Union Annual Session 2016, Dedicated to the 110th anniversary of A. Shahinyan, Abstracts , pp. 18, (2016)
- , On harmonic conjugates in weighted Dirichlet spaces of quaternion-valued functions , International Conference Harmonic Analysis and Approximations, VI, 12--18 September 2015, Tsaghkadzor, Armenia, Abstracts, pp. 17-18, (2015)
- , On weighted Dirichlet spaces in the ball, Armenian Mathematical Union Annual Session 2015, Dedicated to 100th anniversary of H. Badalyan, Abstracts, pp. 16, (2015)
- , On construction of a monogenic function by its first component, Armenian Mathematical Union Annual Session, 4-6 Oct. 2014, Abstracts, pp. 11, (2014)
- , On construction of a monogenic function by its first component, with applications [in Russian], Fifth Russian-Armenian workshop on mathematical physics, complex analysis and related topics, 28 Sep.--3 Oct. 2014, Yerevan, Armenia, Abstracts, pp. 9, (2014)
- , A monogenic version of Riesz theorem on harmonic conjugates, International Congress of Mathematicians, ICM 2014, August 13--21, 2014, Seoul, Korea, Abstracts, pp. 210-211, (2014)
- , On Bergman type projections over Besov and mixed norm spaces, Second International Conference Mathematics in Armenia, Advances and Perspectives, 24 - 31 August 2013, Tsaghkadzor, Armenia, Dedicated to the 70th Anniversary of Foundation of Armenian National Academy of Sciences, Abstracts, Yerevan , pp. 24, (2013)
- , On 3D Riesz systems of harmonic conjugates, 9th Int. Conf. on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA, Vienna, 2012, AIP Conference Proceedings, 1493, pp. 441-445, (2012)
- , Harmonic conjugates in weighted Hardy spaces of quaternion-valued functions, 9th Int. Conference on Clifford Algebras and their Applications, Weimar, Germany, 2011, July 15-20, Summaries, Bauhaus Univ. Weimar, pp. 12, (2011)
- , Some extensions of the Hardy-Littlewood inequalities for harmonic functions, Int. Conf. Harmonic Analysis and Approximations, V, dedicated to 75th anniversary of academician N. Arakelian, 2011, Tsaghkadzor, Armenia, Abstracts, Yerevan, pp. 17-18, (2011)
- , Quaternion-valued harmonic conjugates in weighted Hardy spaces, Third Russian-Armenian workshop on mathematical physics, complex analysis and related topics, Tsaghkadzor, Armenia, 4-8 October, 2010, pp. 34-37, (2010)
- , Lacunary series in weighted spaces of analytic functions, Conference dedicated to 90th anniversary of foundation of Yerevan State University, Abstracts, pp. 15-16, (2009)
- , Sharp inclusions in mixed norm spaces of analytic functions, Conference dedicated to 80th anniversary of academician S. Mergelyan, Abstracts, Yerevan, pp. 8-9, (2008)
- , Lacunary series in mixed norm spaces, Int. Conf. Harmonic Analysis and Approximations, IV, dedicated to 80th anniversary of academician A. Talalian, 2008, Tsaghkadzor, Armenia, Abstracts , pp. 21-22, (2008)
- , A characterization of Bergman spaces $H^p_\omega$ , Academician A. Shahinian Centennial Conference, Abstracts, Yerevan , pp. 5-6, (2006)
- , A maximal theorem for a weighted space on the unit ball of $R^n$, Int. Conf. Harmonic Analysis and Approximations, III, 2005, Tsahkadzor, Armenia, Abstracts, Yerevan, pp. 10-11, (2005)
- , A maximal function characterization of harmonic Bergman spaces, Proc. ISAAC Conf. on Analysis, Yerevan, Armenia, 2002, Gitutjun, pp. 211-217, (2004)
- , Bergman type operators in n-harmonic mixed norm spaces on the polydisc, International Conference Mathematics in Armenia. Advances and Perspectives. Abstracts, Armenia, pp. 20, (2003)
- , Some new integral representations in the classes $H_\alpha^p$ of M. M. Djrbashian, International Conference DMC-98, Abstracts, Yerevan, pp. 7-8, (1998)
- , Green type potentials and representability of some weighted classes of subharmonic functions, Theory of Functions and Applications, Collections of works dedicated to the memory of M. M. Djrbashian, Yerevan, Louys, pp. 11-16, (1995)