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On some properties of multiple conjugate trigonometric series

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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,\(i = \overline {1,n} \)) 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 them λ-convergence (λ≥1) of (C, α) means (α1 > 0,\(i = \overline {1,n} \)) provided that the essential conditions are imposed on the partial moduli of continuity. Finally, it is shown that them λ-convergence cannot be replaced by ordinary convergence.

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Leladze, D. On some properties of multiple conjugate trigonometric series. Georgian Mathematical Journal 1, 287–302 (1994). https://doi.org/10.1007/BF02254677

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1991 Mathematics Subject Classification

  • 42B08