Pointwise strong approximation of almost periodic functions in S^1
We consider the class GM(2b) in pointwise estimate of the deviations in strong mean of S^1 almost periodic functions from matrix means of partial sums of their Fourier series.
A NEW EXTENSION OF MONOTONE SEQUENCES AND ITS APPLICATIONS
We define a new class of numerical sequences. This class is wider than any one of the classical or recently defined new classes of sequences of monotone type. Because of this generality we can generalize only the sufficient part of the classical Chaundy-Jolliffe theorem on the uniform convergence of sine series. We also present two further theorems having conditions of sufficient type.
On double cosine, sine, and Walsh series with monotone coefficients
We extend from one-dimensional to two-dimensional series the results by Hardy and Littlewood [6] on the Lr-integrability of the sum f and the results by Stechkin [10] on the L'-integrability of the maximum partial sum M* in the case of cosine and sine series with monotone coefficients. Among others, we prove that the Lr-integrability of f and M* is essentially equivalent for r > 1 in the two-dimensional setting, too. Simultaneously, we extend our earlier results in [7] from one-dimensional to two-dimensional Walsh series.