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Tephnadze, George
Publications (10 of 26) Show all publications
Persson, L.-E., Tephnadze, G. & Wall, P. (2018). On an approximation of 2-dimensional Walsh–Fourier series in martingale Hardy spaces. Annals of Functional Analysis, 9(1), 137-150
Open this publication in new window or tab >>On an approximation of 2-dimensional Walsh–Fourier series in martingale Hardy spaces
2018 (English)In: Annals of Functional Analysis, ISSN 2008-8752, E-ISSN 2008-8752, Vol. 9, no 1, p. 137-150Article in journal (Refereed) Published
Abstract [en]

In this paper, we investigate convergence and divergence of partial sums with respect to the 2-dimensional Walsh system on the martingale Hardy spaces. In particular, we find some conditions for the modulus of continuity which provide convergence of partial sums of Walsh-Fourier series. We also show that these conditions are in a sense necessary and suffcient. 

Place, publisher, year, edition, pages
Duke University Press, 2018
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-63509 (URN)10.1215/20088752-2017-0032 (DOI)000432617900012 ()2-s2.0-85041646355 (Scopus ID)
Note

Validerad;2018;Nivå 2;2018-02-19 (svasva)

Available from: 2017-05-23 Created: 2017-05-23 Last updated: 2018-06-08Bibliographically approved
Tephnadze, G. (2018). On the Convergence of Partial Sums with Respect to Vilenkin System on the Martingale Hardy Spaces. Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 53(5), 294-306
Open this publication in new window or tab >>On the Convergence of Partial Sums with Respect to Vilenkin System on the Martingale Hardy Spaces
2018 (English)In: Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), ISSN 1068-3623, Vol. 53, no 5, p. 294-306Article in journal (Refereed) Published
Abstract [en]

In this paper, we derive characterizations of boundedness of subsequences of partial sums with respect to Vilenkin system on the martingale Hardy spaces Hp when 0 < p < 1. Moreover, we find necessary and sufficient conditions for the modulus of continuity of martingales f ∈ Hp, which provide convergence of subsequences of partial sums on the martingale Hardy spaces Hp. It is also proved that these results are the best possible in a special sense. As applications, some known and new results are pointed out. 

Place, publisher, year, edition, pages
Springer, 2018
Keywords
Vilenkin system, partial sums, martingale Hardy space, modulus of continuity
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-71832 (URN)10.3103/S1068362318050072 (DOI)000450525500007 ()2-s2.0-85056725514 (Scopus ID)
Note

Validerad;2018;Nivå 2;2018-11-30 (svasva)

Available from: 2018-11-30 Created: 2018-11-30 Last updated: 2019-01-10Bibliographically approved
Persson, L.-E., Tephnadze, G. & Wall, P. (2018). On the Nörlund logarithmic means with respect to Vilenkin system in the Martingale Hardy Space H1. Acta Mathematica Hungarica, 154(2), 289-301
Open this publication in new window or tab >>On the Nörlund logarithmic means with respect to Vilenkin system in the Martingale Hardy Space H1
2018 (English)In: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 154, no 2, p. 289-301Article in journal (Refereed) Published
Abstract [en]

We prove and discuss a new divergence result of Nörlund logarithmic means with respect to Vilenkin system in Hardy space H1.

Place, publisher, year, edition, pages
Springer, 2018
Keywords
Vilenkin system, Nörlund logarithmic mean, partial sum, modulus of continuity, Hardy space
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-66424 (URN)10.1007/s10474-017-0773-8 (DOI)000427375600003 ()
Note

Validerad;2018;Nivå 2;2018-03-14 (rokbeg)

Available from: 2017-11-07 Created: 2017-11-07 Last updated: 2018-04-03Bibliographically approved
Blahota, I., Persson, L.-E. & Tephnadze, G. (2018). Two-sided Estimates of the Lebesgue Constants with respect to Vilenkin Systems and Applications. Glasgow Mathematical Journal, 60(1), 17-34
Open this publication in new window or tab >>Two-sided Estimates of the Lebesgue Constants with respect to Vilenkin Systems and Applications
2018 (English)In: Glasgow Mathematical Journal, ISSN 0017-0895, E-ISSN 1469-509X, Vol. 60, no 1, p. 17-34Article in journal (Refereed) Published
Abstract [en]

In this paper, we derive two-sided estimates of the Lebesgue constants for bounded Vilenkin systems, we also present some applications of importance, e.g., we obtain a characterization for the boundedness of a subsequence of partial sums with respect to Vilenkin–Fourier series of H1 martingales in terms of n's variation. The conditions given in this paper are in a sense necessary and sufficient.

Place, publisher, year, edition, pages
Cambridge University Press, 2018
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-62539 (URN)10.1017/S0017089516000549 (DOI)000417506500002 ()2-s2.0-85015049994 (Scopus ID)
Note

Validerad;2018;Nivå 2;2017-12-14 (svasva)

Available from: 2017-03-16 Created: 2017-03-16 Last updated: 2018-01-10Bibliographically approved
Buchukuri, T., Dudachava, R. & Tephnadze, G. (2017). Laplace–Beltrami equation on hypersurfaces and Γ-convergence. Mathematical methods in the applied sciences, 40(13), 4637-4657
Open this publication in new window or tab >>Laplace–Beltrami equation on hypersurfaces and Γ-convergence
2017 (English)In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 40, no 13, p. 4637-4657Article in journal (Refereed) Published
Abstract [en]

A mixed boundary value problem for the stationary heat transfer equation in a thin layer around a surface C with the boundary is investigated. The main objective is to trace what happens in Γ-limit when the thickness of the layer converges to zero. The limit Dirichlet BVP for the Laplace–Beltrami equation on the surface is described explicitly, and we show how the Neumann boundary conditions in the initial BVP transform in the Γ-limit. For this, we apply the variational formulation and the calculus of Günter's tangential differential operators on a hypersurface and layers, which allow global representation of basic differential operators and of corresponding boundary value problems in terms of the standard Euclidean coordinates of the ambient space Rn.

Place, publisher, year, edition, pages
John Wiley & Sons, 2017
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-62549 (URN)10.1002/mma.4331 (DOI)000405559900001 ()2-s2.0-85017371158 (Scopus ID)
Note

Validerad; 2017; Nivå 2; 2017-08-16 (andbra)

Available from: 2017-03-17 Created: 2017-03-17 Last updated: 2018-07-10Bibliographically approved
Blahota, I. & Tephnadze, G. (2016). A note on maximal operators of Vilenkin-Nörlund means. Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, 32(12), 203-213
Open this publication in new window or tab >>A note on maximal operators of Vilenkin-Nörlund means
2016 (English)In: Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, ISSN 1786-0091, E-ISSN 1786-0091, Vol. 32, no 12, p. 203-213Article in journal (Refereed) Published
Abstract [en]

In this paper we prove and discuss some new (Hp;Lp)-type inequalities of weighted maximal operators of Vilenkin - Nörlund means with non-increasing coeffcients. These results are the best possible in a special sense. As applications, both some well-known and new results are pointed out in the theory of strong convergence of Vilenkin - Nörlund means with non-increasing coeffcients

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-61282 (URN)2-s2.0-85005943522 (Scopus ID)
Note

Validerad; 2017; Nivå 1; 2016-12-29 (andbra)

Available from: 2016-12-29 Created: 2016-12-29 Last updated: 2017-11-29Bibliographically approved
Memić, N., Persson, L.-E. & Tephnadze, G. (2016). A note on the maximal operators of Vilenkin-Nörlund means with non-increasing coefficients (ed.). Studia scientiarum mathematicarum Hungarica (Print), 53(4), 545-556
Open this publication in new window or tab >>A note on the maximal operators of Vilenkin-Nörlund means with non-increasing coefficients
2016 (English)In: Studia scientiarum mathematicarum Hungarica (Print), ISSN 0081-6906, E-ISSN 1588-2896, Vol. 53, no 4, p. 545-556Article in journal (Refereed) Published
Abstract [en]

In [14] we investigated some Vilenkin—Nörlund means with non-increasing coefficients. In particular, it was proved that under some special conditions the maximal operators of such summabily methods are bounded from the Hardy space H1/(1+α) to the space weak-L1/(1+α), (0 < α ≦ 1). In this paper we construct a martingale in the space H1/(1+α), which satisfies the conditions considered in [14], and so that the maximal operators of these Vilenkin—Nörlund means with non-increasing coefficients are not bounded from the Hardy space H1/(1+α) to the space L1/(1+α). In particular, this shows that the conditions under which the result in [14] is proved are in a sense sharp. Moreover, as further applications, some well-known and new results are pointed out.

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-8860 (URN)10.1556/012.2016.53.4.1342 (DOI)000388813600007 ()2-s2.0-84996837296 (Scopus ID)76930bce-6769-4330-b68b-b1c2a6227492 (Local ID)76930bce-6769-4330-b68b-b1c2a6227492 (Archive number)76930bce-6769-4330-b68b-b1c2a6227492 (OAI)
Note

Validerad; 2016; Nivå 2; 2016-12-05 (inah)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Persson, L.-E. & Tephnadze, G. (2016). A Sharp Boundedness Result Concerning Some Maximal Operators of Vilenkin–Fejér Means (ed.). Mediterranean Journal of Mathematics, 13(4), 1841-1853
Open this publication in new window or tab >>A Sharp Boundedness Result Concerning Some Maximal Operators of Vilenkin–Fejér Means
2016 (English)In: Mediterranean Journal of Mathematics, ISSN 1660-5446, E-ISSN 1660-5454, Vol. 13, no 4, p. 1841-1853Article in journal (Refereed) Published
Abstract [en]

In this paper, we derive the maximal subspace of positive numbers, for which the restricted maximal operator of Fejér means in this subspace is bounded from the Hardy space Hp to the space Lp for all 0 < p ≤ 1/2. Moreover, we prove that the result is in a sense sharp

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-14927 (URN)10.1007/s00009-015-0565-8 (DOI)000380671700028 ()2-s2.0-84928969252 (Scopus ID)e5da1a84-3d0b-4257-b89a-d2ca16e7a01a (Local ID)e5da1a84-3d0b-4257-b89a-d2ca16e7a01a (Archive number)e5da1a84-3d0b-4257-b89a-d2ca16e7a01a (OAI)
Note

Validerad; 2016; Nivå 2; 20150519 (andbra)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Tephnadze, G. (2016). On the convergence of Fejér means of Walsh-Fourier series in the space H p (ed.). Paper presented at . Journal of Contemporary Mathematical Analysis, 51(2), 90-102
Open this publication in new window or tab >>On the convergence of Fejér means of Walsh-Fourier series in the space H p
2016 (English)In: Journal of Contemporary Mathematical Analysis, ISSN 1068-3623, Vol. 51, no 2, p. 90-102Article in journal (Refereed) Published
Abstract [en]

The main aim of this paper is to find necessary and sufficient conditions for a modulus of continuity of a martingale F ∈ Hp, for which the Fejér means of Walsh-Fourier series converge in Hp-norm, when 0 < p ≤ 1/2.

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-5286 (URN)10.3103/S1068362316020059 (DOI)000376035000005 ()2-s2.0-84969584380 (Scopus ID)358ae2ee-c675-471c-aadd-a56c9a776273 (Local ID)358ae2ee-c675-471c-aadd-a56c9a776273 (Archive number)358ae2ee-c675-471c-aadd-a56c9a776273 (OAI)
Note
Validerad; 2016; Nivå 2; 20160602 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved
Baramidze, L., Persson, L.-E., Tephnadze, G. & Wall, P. (2016). Sharp Hp- Lptype inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications. Journal of inequalities and applications (Print) (1), Article ID 242.
Open this publication in new window or tab >>Sharp Hp- Lptype inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications
2016 (English)In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, no 1, article id 242Article in journal (Refereed) Published
Abstract [en]

We prove and discuss some new Hp-Lptype inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed out

National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-60035 (URN)10.1186/s13660-016-1182-1 (DOI)000391727200001 ()2-s2.0-84989350634 (Scopus ID)
Note

Validerad; 2016; Nivå 2; 2016-10-31 (andbra)

Available from: 2016-10-31 Created: 2016-10-31 Last updated: 2018-07-10Bibliographically approved
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