2019
Том 71
№ 6

All Issues

Kolyada V. I.

Articles: 3
Article (English)

On Cèsaro and Copson norms of nonnegative sequences

Kolyada V. I.

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 2. - pp. 220-229

The C`esaro and Copson norms of a nonnegative sequence are lp-norms of its arithmetic means and the corresponding conjugate means. It is well known that, for $1 < p < \infty$, these norms are equivalent. In 1996, G. Bennett posed the problem of finding the best constants in the associated inequalities. The solution of this problem requires the evaluation of four constants. Two of them were found by G. Bennett. We find one of the two unknown constants and also prove one optimal weighted-type estimate regarding the remaining constant.

Article (Russian)

Mean oscillations and the convergence of Poisson integrals

Kolyada V. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 2. - pp. 206–222

We establish conditions for mean oscillations of a periodic summable function under which the summability of its Fourier series (conjugate series) by the Abel-Poisson method at a given point implies the convergence of Steklov means (the existence of the conjugate function) at the indicated point. Similar results are also obtained for the Poisson integral in ℝ+n+1.

Article (Ukrainian)

On the rate of convergence of orthogonal series

Kolyada V. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1973. - 25, № 1. - pp. 25-38