On some properties of multiple conjugate trigonometric series

We have obtained an estimate, in terms of partial and mixed moduli, of the continuity of deviation of the Cesáro (C, α) means (α = (α1,...,αn),αi∈ ℝ, α1 > −1,) of the sequence of rectangular partial sums ofn-multiple (n>1) conjugate trigonometric series from then-multiple truncated conjugate function. This estimate implies the result on themλ-convergence (λ≥1) of (C, α) means (α1 > 0,) provided that the essential conditions are imposed on the partial moduli of continuity. Finally, it is shown that themλ-convergence cannot be replaced by ordinary convergence.