# Grigori Karagulyan's Publications (Full profile)

### Paper

- An abstract theory of singular operators, to appear in Trans. Amer. Math. Soc., 372, (1), pp. 4761-4802, (2019)
- On the exponential summability of rectangular partial sums of double trigonometric Fourier series, Mat. Zametki, 104, (5), pp. 667–679, (2018)
- On exceptional sets of the Hilbert transform, Real Anal. Exchange, 42, (2), pp. 311–327, (2017)
- On an equivalence for differentiation bases of dyadic rectangles, Colloq. Math., 146, (2), pp. 295-307, (2017)
- On a theorem of Littlewood, Hokkaido Mathematical Journal , 46, (1), (2017)
- On the divergence of triangular and eccentric spherical sums of double Fourier series, Sbornik Math., 207, (1), pp. 65-84, (2016)
- On convergence properties of tensor products of some operator sequences, J. Geometric Analysis, 26, (4), pp. 3066–3089, (2016)
- On everywhere divergence of the strong Φ-means of Walsh–Fourier series, J. Mathematical Analysis and Applications, 421, (1), pp. 206-214, (2015)
- On Generalizations of Fatou’s Theorem for Integrals with General Kernels, J. Geometric Analysis, 25, (3), pp. 1459-1475, (2015)
- On divergence triangular sums of double Fourier series, J. Contemporary Math. Analysis, 50, (4), pp. 196-207, (2015)
- BMO-estimation and almost everywhere exponential summability of quadratic partial sums of double Fourier series, Constructive Approximation, 40, (1), pp. 105-120, (2014)
- On the Divergence of Triangular and Sectorial Sums of Double Fourier Series, Dokl. NAS of Armenia, 114, (2), pp. 98-100, (2014)
- On the divergence of Walsh and Haar series by sectorial and triangular regions, Proc. Yerevan State Univ., 234, (2), pp. 3-12, (2014)
- On the characterization of extremal sets in the theory of differentiation of integrals, J. Contemporary Math. Analysis, 48, (6), pp. 334-351, (2014)
- A remark on the divergence of strong power means of Walsh-Fourier series, Math. Notes, 96, (6), pp. 59-65, (2014)
- Almost everywhere strong summability of Marcinkiewicz strong means of double Walsh-Fourier series, Analysis Mathematica, 40, (4), pp. 243-266, (2014)
- On classes of everywhere divergent power series, Acta Mathematica Hungarica, 140, (1-2), pp. 36-46, (2013)
- On equivalency of martingales and related problems, J. Contemporary Math. Analysis, 48, (2), pp. 51-65, (2013)
- Characterization of the sets of divergence for sequences of operators with the localization property, Mathematical Sbornik, 202, (1), pp. 12-36, (2011)
- On the sweeping out property for convolution operators of discrete measures, Proc. Amer. Math. Soc., 139, (7), pp. 2543-2552, (2011)
- On complete characterization of divergence sets of Fourier-Haar series, J. Contemporary Math. Analysis, 45, (6), pp. 334-347, (2010)
- Divergence of general operators on the sets of measure zero, Colloq. Math., 121, (1), pp. 113-119, (2010)
- On Riemann sums and maximal functions in $R^n$, Mathematical Sbornik, 200, (4), pp. 521-548, (2009)
- On Riemann sums and maximal functions in
$R^n$, Math. Sbornik, 200, (4), pp. pp. 53-82, (2009)
- A complete characterization of R-sets in
the theory of differentiation of integrals,, Studia Math., 181, pp. 17-32, (2007)
- On unboundedness of maximal operators for
directional Hilbert transforms, Proceedings of the AMS, 135, (10), pp. 3133-3141, (2007)
- Everywhere divergent $\Phi $-means of
Fourier series, Mathematical Notes, 80, (1-2), pp. 47-56, (2006)
- An estimate of the maximal
operators associated with generalized lacunary sets, Journal of Contemporary Math. Analysis, 39, (1), pp. 73-83, (2004)
- On the exponential estimates of Calderon-Zygmund operator and related problems of Fourier series, Math. Zametki, 71, (3), pp. 1-14, (2002)
- 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)
- Some linear summation methods for Furier series, Math. Sbornik, 189, (5), pp. 771-795, (1998)
- On divergence almost everywhere of the rectangular partial sums of multiple Fourier series of bounded functions, Math. Zametki, 64, (1), pp. 24-36, (1998)
- On the growth of integral means of functions from $L^1(R^n)$, East Journal on Approx. , 3, (1), pp. 1-12, (1997)
- Hilbert transform and exponential integral estimates of rectangular sums of double Fourier series, Math. Sbornik, 187, (3), pp. 365-384, (1996)
- 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)
- 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)
- On the convergence to infinity of Fourier series along dense sub-sequence of numbers, Analysis Mathematica, 18, (4), pp. 249-259, (1992)
- On the divergence of strong $Phi $-means of Fourier series, Journal of Contemporary Math. Anal. , 26, (2), pp. 159-162, (1991)
- 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)
- On the growth of rectangular integralmeans of functions from $L^1(R^n)$, Dokl. AN of Armenia, 89, (2), pp. 51-53, (1989)
- On the divergence of the double Fourier series by complete orthonormal systems, Journal of Contemporary Math. Anal. , 24, (2), pp. 147-159, (1989)
- On the selection of a convergence subsystem with logarithmic density from an arbitrary orthonormal system, Math. USSR Sbornik, 64, (1), pp. 41-56, (1989)
- On the convergence subsystems of an arbitrary orthonormal system, Acta Sci. Math. , 373-386 (in Russian), 52, (3-4), (1988)
- 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)
- On the equivalent orthogonal systems, Journal of Contemporary Math. Anal. , 22, (5), pp. 510-513, (1987)
- 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)
- On the selection unconditional convergence
subsystems from an orthonormal system from some class, Dokl. AN of, 82, (4), pp. 160-164, (1986)
- On averaging processes of functions of bounded variation, Acta Math. Hung. , 299-300 (in Russian), 48, (3-4), (1986)
- On the convergence by Pringsheim of the double orthogonal series, Journal of Contemporary Math. Anal. , 21, (1), pp. 80-99, (1986)

### Book

- Lectures on Singular Operators, (2018)

### Preprint

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

### Thesis

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