# Grigori Karagulyan's Publications (Full profile)

### Paper

1. Grigori A. Karagulyan, Michael T. Lacey, On logarithmic bounds of maximal sparse operators, Mathematische Zeitschrift, 294, (3-4), pp. 1271-1281, (2020)
2. Grigori A. Karagulyan, Menshov type correction theorems for sequences of compact operators, Constructive Approximation, 51, (2), pp. 331–352, (2020)
3. Grigori A. Karagulyan and Gevorg Mnatsakanyan, On a weak type estimate for sparse operators of strong type, Journal of Contemporary Math. Analysis, 54, (4), pp. 36-44, (2019)
4. G. A. Karagulyan, H. A. Mkoyan, An exponential estimate for the cubic partial sums of multiple Fourier series, Izv. Math., 83, (2), pp. 273–286 , (2019)
5. Grigori A. Karagulyan, An abstract theory of singular operators, Trans. Amer. Math. Soc., 372, (7), pp. 4761-4802, (2019)
6. U. Goginava, G. A. Karagulyan, On the exponential summability of rectangular partial sums of double trigonometric Fourier series, Mat. Zametki, 104, (5), pp. 667–679, (2018)
7. Grigori A. Karagulyan, On exceptional sets of the Hilbert transform, Real Anal. Exchange, 42, (2), pp. 311–327, (2017)
8. G. A. Karagulyan, D. A. Karagulyan, M. H. Safaryan, On an equivalence for differentiation bases of dyadic rectangles, Colloq. Math., 146, (2), pp. 295-307, (2017)
9. G. A. Karagulyan, M. H. Safaryan, On a theorem of Littlewood, Hokkaido Mathematical Journal , 46, (1), (2017)
10. G. A. Karagulyan, On the divergence of triangular and eccentric spherical sums of double Fourier series, Sbornik Math., 207, (1), pp. 65-84, (2016)
11. G. Gat, G. Karagulyan, On convergence properties of tensor products of some operator sequences, J. Geometric Analysis, 26, (4), pp. 3066–3089, (2016)
12. G. Gat, U. Goginava, G. Karagulyan, On everywhere divergence of the strong Φ-means of Walsh–Fourier series, J. Mathematical Analysis and Applications, 421, (1), pp. 206-214, (2015)
13. G. A. Karagulyan, M. H. Safaryan, On Generalizations of Fatou’s Theorem for Integrals with General Kernels, J. Geometric Analysis, 25, (3), pp. 1459-1475, (2015)
14. G. A. Karagulyan, K. R. Muradyan, On divergence triangular sums of double Fourier series, J. Contemporary Math. Analysis, 50, (4), pp. 196-207, (2015)
15. U. Goginava, L. Gogoladze, G. Karagulyan, BMO-estimation and almost everywhere exponential summability of quadratic partial sums of double Fourier series, Constructive Approximation, 40, (1), pp. 105-120, (2014)
16. G. A. Karagulyan, K. R. Muradyan, On the Divergence of Triangular and Sectorial Sums of Double Fourier Series, Dokl. NAS of Armenia, 114, (2), pp. 98-100, (2014)
17. G. A. Karagulyan, K. R. Muradyan, On the divergence of Walsh and Haar series by sectorial and triangular regions, Proc. Yerevan State Univ., 234, (2), pp. 3-12, (2014)
18. G. A. Karagulyan, D. A. Karagulyan, On the characterization of extremal sets in the theory of differentiation of integrals, J. Contemporary Math. Analysis, 48, (6), pp. 334-351, (2014)
19. G. Gat, U. Goginava, G. Karagulyan, A remark on the divergence of strong power means of Walsh-Fourier series, Math. Notes, 96, (6), pp. 59-65, (2014)
20. G. Gat, U. Goginava, G. Karagulyan, Almost everywhere strong summability of Marcinkiewicz strong means of double Walsh-Fourier series, Analysis Mathematica, 40, (4), pp. 243-266, (2014)
21. G. A. Karagulyan, On classes of everywhere divergent power series, Acta Mathematica Hungarica, 140, (1-2), pp. 36-46, (2013)
22. G. A. Karagulyan, On equivalency of martingales and related problems, J. Contemporary Math. Analysis, 48, (2), pp. 51-65, (2013)
23. G. A. Karagulyan, Characterization of the sets of divergence for sequences of operators with the localization property, Mathematical Sbornik, 202, (1), pp. 12-36, (2011)
24. G. A. Karagulyan, On the sweeping out property for convolution operators of discrete measures, Proc. Amer. Math. Soc., 139, (7), pp. 2543-2552, (2011)
25. G. A. Karagulyan, On complete characterization of divergence sets of Fourier-Haar series, J. Contemporary Math. Analysis, 45, (6), pp. 334-347, (2010)
26. G. A. Karagulyan, Divergence of general operators on the sets of measure zero, Colloq. Math., 121, (1), pp. 113-119, (2010)
27. G. A. Karagulyan, On Riemann sums and maximal functions in $R^n$, Mathematical Sbornik, 200, (4), pp. 521-548, (2009)
28. G. A. Karagulyan, On Riemann sums and maximal functions in $R^n$, Math. Sbornik, 200, (4), pp. pp. 53-82, (2009)
29. G.A. Karagulyan, A complete characterization of R-sets in the theory of differentiation of integrals,, Studia Math., 181, pp. 17-32, (2007)
30. G.A. Karagulyan, On unboundedness of maximal operators for directional Hilbert transforms, Proceedings of the AMS, 135, (10), pp. 3133-3141, (2007)
31. G.A. Karagulyan, Everywhere divergent $\Phi$-means of Fourier series, Mathematical Notes, 80, (1-2), pp. 47-56, (2006)
32. G.A. Karagulyan, M.T.Lacey, An estimate of the maximal operators associated with generalized lacunary sets, Journal of Contemporary Math. Analysis, 39, (1), pp. 73-83, (2004)
33. G. A. Karagulyan, On the exponential estimates of Calderon-Zygmund operator and related problems of Fourier series, Math. Zametki, 71, (3), pp. 1-14, (2002)
34. G. A. Karagulyan, On the exponential estimates of partial sums of Fourier series by Walsh system and rearranged Haar system, Journal of Contemporary Math. Anal. , 36, (5), pp. 23-34, (2001)
35. A. A. Talalyan, G. G. Gevorkyan, G. A. Karagulyan, Some linear summation methods for Furier series, Math. Sbornik, 189, (5), pp. 771-795, (1998)
36. S. Sh. Galstyan, G. A. Karagulyan, On divergence almost everywhere of the rectangular partial sums of multiple Fourier series of bounded functions, Math. Zametki, 64, (1), pp. 24-36, (1998)
37. G. A. Karagulyan, On the growth of integral means of functions from $L^1(R^n)$, East Journal on Approx. , 3, (1), pp. 1-12, (1997)
38. G. A. Karagulyan, Hilbert transform and exponential integral estimates of rectangular sums of double Fourier series, Math. Sbornik, 187, (3), pp. 365-384, (1996)
39. G. A. Karagulyan, On the order of growth $o(loglog n)$ of the partial sums of Fourier-Stieltjes series of random measures, Russian Acad. Sci. Sb. Math. , 78, (1), pp. 11-33, (1994)
40. G. A. Karagulyan, On the convergence in $L^p$ of the orthogonal series on the sets of full measure, Journal of Contemporary Math. Anal. , 29, (2), pp. 59-66, (1994)
41. G. A. Karagulyan, On the convergence to infinity of Fourier series along dense sub-sequence of numbers, Analysis Mathematica, 18, (4), pp. 249-259, (1992)
42. G. A. Karagulyan, On the divergence of strong $Phi$-means of Fourier series, Journal of Contemporary Math. Anal. , 26, (2), pp. 159-162, (1991)
43. G. A. Karagulyan, A nessesary and sufficient condition for differentiation of in integrals of random measures in $R^n$ by $n$- dimensional intervals, Math. Zametki, 49, (4), pp. 63-68, (1991)
44. G. A. Karagulyan, On the growth of rectangular integralmeans of functions from $L^1(R^n)$, Dokl. AN of Armenia, 89, (2), pp. 51-53, (1989)
45. G. A. Karagulyan, On the divergence of the double Fourier series by complete orthonormal systems, Journal of Contemporary Math. Anal. , 24, (2), pp. 147-159, (1989)
46. G. A. Karagulyan, On the selection of a convergence subsystem with logarithmic density from an arbitrary orthonormal system, Math. USSR Sbornik, 64, (1), pp. 41-56, (1989)
47. G. A. Karagulyan, On the convergence subsystems of an arbitrary orthonormal system, Acta Sci. Math. , 373-386 (in Russian), 52, (3-4), (1988)
48. G. A. Karagulyan, On the selection convergence subsystems with lacunary density of numbers from an arbitrary orthonormal systems, Dokl. AN of Armenia, 84, (1), pp. 17-20, (1987)
49. G. A. Karagulyan, On the equivalent orthogonal systems, Journal of Contemporary Math. Anal. , 22, (5), pp. 510-513, (1987)
50. G. A. Karagulyan, On the selection unconditional convergence subsystems from an orthonormal system from some class, Dokl. AN of, 82, (4), pp. 160-164, (1986)
51. G. A. Karagulyan, On averaging processes of functions of bounded variation, Acta Math. Hung. , 299-300 (in Russian), 48, (3-4), (1986)
52. G. A. Karagulyan, On the convergence by Pringsheim of the double orthogonal series, Journal of Contemporary Math. Anal. , 21, (1), pp. 80-99, (1986)
53. G. A. Karagulyan, On the convergence subsystems and divergence double Fourier series by complete orthonormal systems 1986, Vol. 82, No 3, 112-115.(in Russian), Dokl. AN of Armenia, 82, (3), pp. 112-115, (1986)

### Book

1. Grigori A. Karagulyan, Lectures on Singular Operators, (2018)

### Preprint

1. G. A. Karagulyan, On Riemann sums and maximal functions in $R^n$, http:// arxiv.org/abs/math/0803.4392, (2008)
2. G.A. Karagulyan, On unboundedness of maximal operators for directional Hilbert transforms, http://arxiv.org/abs/math/0602524, (2006)
3. G.A. Karagulyan, On the characterization of differentiation sets of integrals, http://arxiv.org/abs/math/0511479, (2005)
4. G.A. Karagulyan and M.T.Lacey, Littlewood--Paley inequalities and maximal functions in higher dimensions, http://arxiv.org/abs/math/0404027, (2003)

### Thesis

1. G. A. Karagulyan, Basis of rectangles and differentiation of integrals, Thesises of International Conference of Harmonic III, (2005)
2. G. A. Karagulyan, Maximal functions and lacunary sets , International Conference of Approximation Theory dedicated to 100-aniversary of S. M. Nikolski, Moscow, (2005)
3. A. Karagulyan, M. Lacey, On Estimates of Maximal Operators along directions and High dimentional Littlewood-Paley inequalities , Thesises of International Conference Mathematics in Armenia, Armenia, Tsahchadzor, (2003)
4. G. A. Karagulyan, On estimate of conjugate function by maximal function, Thesises of International Conference of Harmonic Analysis and Approximations II, Armenia, Nor Amberd, (2001)
5. G. A. Karagulyan, On the growth of partial sums of multiple Fourier series , International Congress of Mathematics, Zurich, (1994)