Larry Gogoladze

Strong Approximation by Marcinkiewicz Means of Two-dimensional Walsh-Fourier Series

In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh-Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh-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.

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

On the constancy of signs and order of magnitude of Fourier–Haar coefficients

left( {mathbb{T}^2 } right)

Convergence in measure of logarithmic means of multiple Fourier series

into space Lp

Summability of multiple trigonometric Fourier series by linear methods

left( {mathbb{T}^2 } right)

BMO-Estimation and Almost Everywhere Exponential Summability of Quadratic Partial Sums of Double Fourier Series

, 0 < p < 1, are studied. The maximal Orlicz space such that the Nörlund strong logarithmic means of double Fourier series for the functions from this space converge in two-dimensional measure is found.