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Acta Mathematica Sinica,English Series 2011年第10期27卷 1949-1958页

作者： ushangi goginava Institute of Mathematics Faculty of Exact and Natural Sciences Tbilisi State University Chavchavadze str. 1 Tbilisi 0128 Georgia

The main aim of this paper is to prove that for any 0 〈 p≤ 2/3 there exists a martingale f E Hp such that Marcinkiewicz Fejer means of the two-dimensional conjugate Walsh Fourier series of the martingale f is not un... 详细信息

关键词： Two-dimensional Walsh-Fourier series martingale Hardy space Marcinkiewicz Fejer means

THE HARDY TYPE INEQUALITY FOR THE MAXIMAL OPERATOR OF THE ONE-DIMENSIONAL DYADIC DERIVATIVE

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Acta Mathematica Scientia 2011年第4期31卷 1489-1493页

作者： ushangi goginava Institute of Mathematics Faculty of Exact and Natural Sciences Tbilisi State University

In this paper we prove that the maximal operator I of dyadic derivative is not bounded from the Hardy space H p [0, 1] to the Hardy space H p [0, 1], when 0 〈 p ≤ 1.

关键词： Walsh function Hardy space dyadic derivative

WEAK TYPE INEQUALITY FOR THE MAXIMAL OPERATOR OF WALSH-KACZMARZ-MARCINKIEWICZ MEANS

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Acta Mathematica Scientia 2016年第2期36卷 359-370页

作者： ushangi goginava Karoly NAGY Department of Mechanics and Mathematics Tbilisi State University Chavchavadze str. 1 Tbilisi 0128 Georgia Institute of Mathematics and Computer Sciences College of Nyiregyhdza SSstSi str. 31/B 4400 Nyiregyhdza Hungary

The main aim of this article is to prove that the maximal operator σ^k＊ of the Marcinkiewicz-Fejer means of the two-dimensional Fourier series with respect to Walsh- Kaczmarz system is bounded from the Hardy space H... 详细信息

关键词： Walsh-Kaczmarz system Marcinkiewicz-Fej^r means Maximal operator a.e.convergence weak type inequality

On the Divergence of N(?)rlund Logarithmic Means of Walsh-Fourier Series

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Acta Mathematica Sinica,English Series 2009年第6期25卷 903-916页

作者： Gyrgy GAT ushangi goginava Institute of Mathematics and Computer Science College of Nyíregyháza Department of Mechanics and Mathematics Tbilisi State University

It is well known in the literature that the logarithmic means 1/logn ^n-1∑k=1 Sk（f）/k of Walsh or trigonometric Fourier series converge a.e. to the function for each integrable function on the unit interval. This is not the case if we take the partial sums. In this paper we prove that the behavior of the so-called NSrlund logarithmic means 1/logn ^n-1∑k=1 Sk（f）/n-k is closer to the properties of partial sums in this point of view.

关键词： Walsh function Norlund logarithmic means a.e. divergence.

APPROXIMATION PROPERTIES OF (C, α) MEANS OF DOUBLE WALSH-FOURIER SERIES

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Analysis in Theory and Applications 2004年第1期20卷 77-98页

作者： ushangi goginava Tbilisi State University Georgiae study the rate of Lp approximation by Cesaro means of the quadratic partial sums of double Walsh-Fourier series of functions from Lp.

We study the rate of Lp approximation by Cesaro means of the quadratic partial sums of double Walsh-Fourier series of functions from Lp.

关键词： Cesaro means double wallsh-Fourier series

Uniform and L-convergence of Logarithmic Means of Walsh-Fourier Series

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Acta Mathematica Sinica,English Series 2006年第2期22卷 497-506页

作者： G.GáT U.goginava Institute of Mathematics and Computer Science College of Nyiregyhaza Department of Mechanics and Mathematics Tbilisi State University

The （NSrlund） logarithmic means of the Fourier series of the integrable function f is：1/lnn-1∑k=1Sk（f）/n-k, where ln：=n-1∑k=11/k.In this paper we discuss some convergence and divergence properties of this logarithmic means of the Walsh-Fourier series of functions in the uniform, and in the L^1 Lebesgue norm. Among others, as an application of our divergence results we give a negative answer to a question of Móricz concerning the convergence of logarithmic means in norm.

关键词： Walsh system Norlund logarithmic means Convergence divergence properties

UNIFORM CONVERGENCE OF CES■RO MEANS OF NEGATIVE ORDER OF DOUBLE TRIGONOMETRIC FOURIER SERIES

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Analysis in Theory and Applications 2007年第3期23卷 255-265页

作者： U.goginava Tbilisi State University Georgia

In this paper we prove that if f ∈ C （[-π, π]^2） and the function f is bounded partial p-variation for some p ∈[1, ＋∞）, then the double trigonometric Fourier series of a function f is uniformly （C;-α,-β） summable （α＋β 〈 1/p,α,β 〉 0） in the sense of Pringsheim. If α ＋ β ≥ 1/p, then there exists a continuous function f0 of bounded partial p-variation on [-π,π]^2 such that the Cesàro （C;-α,-β） means σn,m^-α,-β（f0;0,0） of the double trigonometric Fourier series of f0 diverge over cubes.

关键词： Fourier series bounded variation. Cesàro means

A NOTE ON THE WALSH-FEJR MEANS

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Analysis in Theory and Applications 2010年第4期26卷 320-325页

作者： Ushahgi goginava Graduate Tbilisi State

The main aim of this paper is to prove that the maximal operator σ# is not bounded from the martingale Hardy space Hp （G） to the martingale Hardy space Hp （G） for 0〈p≤1.

关键词： Walsh function Hardy space Fejer means

CONVERGENCE OF LOGARITHMIC MEANS OF MULTIPLE WALSH-FOURIER SERIES

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Analysis in Theory and Applications 2005年第4期21卷 326-338页

作者： G.Gát U.goginava G.Tkebuchava College of Nyíregyháza Hungary Tbilisi State University Georgia

Norlund logarithmic means of multiple Walsh-Fourier series acting from space L In^d-1 L （[0, 1）d）, d≥1 into space weak - LI（[0,1）^d） are studied. The maximal Orlicz space such that the Norlund logarithmic means... 详细信息

关键词： Multiple Walsh-Fourier series convergence in metric and in measure Norlund means

New Line of Drinks Based on Grape Products

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Journal of Food Science and Engineering 2012年第2期2卷 106-110页

作者： Zaira Shapatava Kukuri Dzeria Lali goginava Zviad Bobokashvili Institute of Horticulture Viticulture and Oenology of the Agricultural University of Georgia Tbilisi 0159 Georgia

Fruit processing is the appropriative way to augment fruit intake. The present paper shows production technology, which is based on the characteristics of selected raw materials and does not use sugar （saccharose）. The objective of the present paper is to produce healthful and disease preventive beverages based on ＂Saperavi＂ red wine and bilberries, using grape juice concentrate and stevioside, a natural sweetener, instead of saccharose. The technology is based on the removal of alcohol at a low temperature and low pressure. In these conditions about 50% of moisture is evaporated. The extract is then diluted with 0.25% of stevioside liquid and the ratio is 1：1. The working name is ＂Saperavi-S＂. Bilberry juice is added to this beverage at the ratio of 1： l in order to enrich it with biologically active substances. The working name of this beverage is ＂Marnidan＂. The products have high contents of phenolic compounds, mainly-anthocyanins. The main idea of technology uses bilberry juice with grape juice concentrate. Bilberries have quite high antioxidant activity, amounting to 55% against l,l-Diphenyl-2-picrylhydrazyl. It is the first time we have produced a beverage based on dealcoholized red wine, stevioside and bilberry juice. This beverage is of special importance in terms of its disease-preventive qualities, including prevention of diabetes, one of the most widespread chronic diseases.

关键词： Antioxidants anthocyanins flavanols non-alcoholic wine beverage bilberry steviosid.