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Tephnadze, George

Open this publication in new window or tab >>On an approximation of 2-dimensional Walsh–Fourier series in martingale Hardy spaces### Persson, Lars-Erik

### Tephnadze, George

### Wall, Peter

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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##### Note

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.

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.

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

Available from: 2017-05-23 Created: 2017-05-23 Last updated: 2018-06-08Bibliographically approvedOpen this publication in new window or tab >>On the Convergence of Partial Sums with Respect to Vilenkin System on the Martingale Hardy Spaces### Tephnadze, George

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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##### Note

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. University of Georgia, Tbilisi, Georgia.

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.

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

Available from: 2018-11-30 Created: 2018-11-30 Last updated: 2019-01-10Bibliographically approvedOpen this publication in new window or tab >>On the Nörlund logarithmic means with respect to Vilenkin system in the Martingale Hardy Space _{H1}### Persson, Lars-Erik

### Tephnadze, George

### Wall, Peter

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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##### Note

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. RUDN University, Moscow, Russia; UiT The Arctic University of Norway.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. School of Informatics, Engineering and Mathematics, The University of Georgia.

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

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

Available from: 2017-11-07 Created: 2017-11-07 Last updated: 2018-04-03Bibliographically approvedOpen this publication in new window or tab >>Two-sided Estimates of the Lebesgue Constants with respect to Vilenkin Systems and Applications### Blahota, I.

### Persson, Lars-Erik

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Tephnadze, George

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_j_idt365",{id:"formSmash:j_idt184:3:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_j_idt365",multiple:true});
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##### Note

Institute of Mathematics and Computer Sciences, University of Nyìıregyhàza.

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.

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

Available from: 2017-03-16 Created: 2017-03-16 Last updated: 2018-01-10Bibliographically approvedOpen this publication in new window or tab >>Laplace–Beltrami equation on hypersurfaces and Γ-convergence### Buchukuri, Tengiz

### Dudachava, Roland

### Tephnadze, George

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_j_idt359",{id:"formSmash:j_idt184:4:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_j_idt359",multiple:true});
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##### Note

A. Razmadze Mathematical Institute, Tbilisi State University.

A. Razmadze Mathematical Institute, Tbilisi State University.

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.

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

Available from: 2017-03-17 Created: 2017-03-17 Last updated: 2018-07-10Bibliographically approvedOpen this publication in new window or tab >>A note on maximal operators of Vilenkin-Nörlund means### Blahota, István

### Tephnadze, George

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2016 (English)In: Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, ISSN 1786-0091, E-ISSN 1786-0091, Vol. 32, no 2, p. 203-213Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Mathematical Analysis
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:ltu:diva-61282 (URN)2-s2.0-85005943522 (Scopus ID)
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##### Note

Institute of Mathematics and Computer Sciences, University of Nyíregyháza.

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

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

Available from: 2016-12-29 Created: 2016-12-29 Last updated: 2020-01-28Bibliographically approvedOpen this publication in new window or tab >>A note on the maximal operators of Vilenkin-Nörlund means with non-increasing coefficients### Memić, Nacima

### Persson, Lars-Erik

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Tephnadze, George

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
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##### Note

Department of mathematics, University of Sarajevo.

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 *H*_{1/(1+α)} to the space weak-*L*_{1/(1+α)}, (0 < *α* ≦ 1). In this paper we construct a martingale in the space *H*_{1/(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 *H*_{1/(1+α)} to the space *L*_{1/(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.

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

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approvedOpen this publication in new window or tab >>A Sharp Boundedness Result Concerning Some Maximal Operators of Vilenkin–Fejér Means### Persson, Lars-Erik

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Tephnadze, George

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
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##### Note

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

Validerad; 2016; Nivå 2; 20150519 (andbra)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approvedOpen this publication in new window or tab >>On the convergence of Fejér means of Walsh-Fourier series in the space H p### Tephnadze, George

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2016 (English)In: Journal of Contemporary Mathematical Analysis, ISSN 1068-3623, Vol. 51, no 2, p. 90-102Article in journal (Refereed) Published
##### Abstract [en]

##### 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)
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##### Note

Validerad; 2016; Nivå 2; 20160602 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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.

Open this publication in new window or tab >>Sharp H_{p}- L_{p}type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications### Baramidze, Lasha

### Persson, Lars-Erik

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Tephnadze, George

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.### Wall, Peter

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
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##### Note

Department of Mathematics, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University.

We prove and discuss some new H_{p}-L_{p}type 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

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

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