arXiv subjects

Ushangi Goginava

Publications and source records attributed to Ushangi Goginava.

34 records · Page 2Linked to original sources

arXiv2016

Strong Approximation by Marcinkiewicz Means of two-dimensional Walsh-Kaczmarz-Fourier Series

In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh-Kaczmarz-Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh-Kaczmarz-Fourier series of the continuous function $f$ is uniformly strong summable to the function $f$ exponentially in the power $1/2$. Moreover, it is proved that this result is best possible.

math.AP↗

arXiv2016

Strong Summability of Two-Dimensional Vilenkin Fourier series

In this paper we study the exponential uniform strong summability of two-dimensional Vilenkin-Fourier series. In particular, it is proved that the two-dimensional Vilenkin-Fourier series of the continuous function $f$ is uniformly strong summable to the function $f$ exponentially in the power $1/2$. Moreover, it is proved that this result is best possible.

math.AP↗

arXiv2016

Almost Everywhere Strong Summability of two-dimensional Walsh-Fourier Series

It is proved a BMO-estimation for quadratic partial sums of two-dimensional Walsh-Fourier series from which it is derived an almost everywhere exponential summability of quadratic partial sums of double Walsh-Fourier series.

math.AP↗

arXiv2014

Convergence and Summability of Multiple Fourier series and generalized variation

In this paper we present results on convergence and Cesàro summability of Multiple Fourier series of functions of bounded generalized variation.

math.AP↗

arXiv2014

On the Convergence and Summability of double Walsh-Fourier series of functions of bounded generalized variation

The convergence of partial sums and Cesáro means of negative order of double Walsh-Fourier series of functions of bounded \ generalized variation is investigated.

math.AP↗

arXiv2014

Convergence of logarithmic means of Multiple Walsh-Fourier series

The maximal Orlicz spaces such that the mixed logarithmic means of multiple Walsh-Fourier series for the functions from these spaces converge in measure and in norm are found.

math.AP↗

arXiv2013

Convergence in Norm of logarithmic means of Multiple Fourier series

The maximal Orlicz space such that the mixed logarithmic means of multiple Fourier series for the functions from this space converge in $L_{1}$-norm is found.

math.AP↗

arXiv2013

Triangular Fejér Summability of Two-Dimensional Walsh-Fourier series

It is proved that the operators $σ_{n}^{\bigtriangleup}$ of the triangular-Fej{é}r-means of a two-dimensional Walsh--Fourier series are uniformly bounded from the dyadic Hardy space $H_{p}$ to $L_{p}$ for all $% 4/5<p\leq \infty $.

math.AP↗

arXiv2013

Relations Between Some Classes Of Functions Of Generalized Bounded Variation

We prove inclusion relations between generalized Waterman's and generalized Wiener's classes for functions of two variable.

math.FA↗

arXiv2013

Convergence in Measure of Strong logarithmic means of double Fourier series

Nörlund strong logarithmic means of double Fourier series acting from space $% L\log L(\mathbb{T}^{2}) $ into space $L_{p}(\mathbb{T}% ^{2}), 0<p<1$ are studied. The maximal Orlicz space such that the Nö% rlund strong logarithmic means of double Fourier series for the functions from this space converge in two-dimensional measure is found.

math.AP↗

arXiv2013

Convergence of logarithmic means of quadratical partial sums of double Fourier series

In this paper we investigate some convergence and divergence properties of the logarithmic means of quadratical partial sums of double Fourier series of functions in the measure and in the $L$ Lebesgue norm.

math.AP↗

arXiv2012

On the convergence of double Fourier series of functions of bounded partial generalized variation

The convergence of double Fourier series of functions of bounded partial $Λ$-variation is investigated. The sufficient and necessary conditions on the sequence $Λ=\{λ_n\}$ are found for the convergence of Fourier series of functions of bounded partial $Λ$-variation.

math.AP↗

arXiv2012

On the convergence of multiple Fourier series of functions of bounded partial generalized variation

The convergence of multiple Fourier series of functions of bounded partial $% Λ$-variation is investigated. The sufficient and necessary conditions on the sequence $Λ=\{λ_n\}$ are found for the convergence of multiple Fourier series of functions of bounded partial $Λ$-variation.

math.AP↗

arXiv2012

On the convergence of Cesàro means of negative order of double trigonometric Fourier series of functions of bounded partial generalized variation

The convergence of Cesàro means of negative order of double trigonometric Fourier series of functions of bounded partial $Λ$-variation is investigated. The sufficient and neccessary conditions on the sequence $Λ=\{λ_{n}\}$ are found for the convergence of Cesàro means of Fourier series of functions of bounded partial $Λ$-variation.

math.AP↗

arXiv2012

Uniform Convergence of Double Fourier-Legendre series of Functions of Bounded Generalized Variation

The Uniform convergence of double Fourier-Legendre series of function of bounded Harmonic variation and bounded partial $Λ$-variation are investigated.

math.AP↗

arXiv2012

Convergence of multiple Fourier series of functions of bounded generalized variation

The paper introduces a new concept of $Λ$-variation of multivariable functions and investigates its connection with the convergence of multidimensional Fourier series

math.AP↗