No abstract

Abstract. We have obtained the estimate in the terms of partial and mixed moduli of continuity of deviation of Cesáro (C, ) means ( = (α 1 , . . . , αn), α i ∈ R, α i > −1, i = 1, n) of the sequence of rectangular partial sums of n-multiple (n > 1) conjugate trigonometric series from n-multiple truncated conjugate function. This estimate implies the result on the m λ -convergence (λ ≥ 1) of (C, ) means (α i > 0, i = 1, n), provided that the essential conditions are imposed on the partial moduli of continuity. Finally, it is shown, that the m λ -convergence cannot be replaced by ordinary convergence.

We have obtained the estimate in the terms of partial and mixed moduli of continuity of deviation of Cesáro (C, ) means of the sequence of rectangular partial sums of n-multiple (n > 1) conjugate trigonometric series from n-multiple truncated conjugate function. This estimate implies the result on the -convergence (⋋ ≥ 1) of (C, ) means , provided that the essential conditions are imposed on the partial moduli of continuity. Finally, it is shown, that the -convergence cannot be replaced by ordinary convergence.