Uniform convergence of trigonometric series with $p$-bounded variation coefficients

A necessary condition for uniform convergence of double sine series with $p$-bounded variation coefficients

“…On the other hand, using n/b 2 (n) = O(1) we have, for any m ∈ N, If j → ∞ and k < max {λ, 2r} or j < max {λ, 2r} and k → ∞, then (2.1) follows from the uniform convergence of the single series (see [8]) analogously to the proof of the result of Kórus and Móricz [7]. This ends the proof.…”

“…A generalization of Theorem 1.1 to the class GM(p, ... β , r) was proved in [8]. Moreover, the necessity of (1.2) for the uniform convergence of (1.1) was proved for sine series with nonnegative coefficients from each of the above classes.…”

“…These classes are larger than the class of monotone sequences and contain sequences of complex numbers as well. The latest class is the following (see [8]):…”