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Weighted integrability of double cosine series with nonnegative coefficients by Chang-Pao Chen and Ming-Chuan Chen (Hsinchu) Abstract. Let fc(x, y) ≡ ∑∞ j=1 ∑∞ k=1 ajk(1 − cos jx)(1 − cos ky) with ajk ≥ 0 for all j, k ≥ 1. We estimate the integral π 0 π 0 xα−1yβ−1φ(fc(x, y)) dx dy in terms of the coefficients ajk, where α, β ∈ R and φ : [0,∞] → [0,∞]. Our results can be regarded as the trigonometric analogues of those of Mazhar and Móricz [MM]. They generalize and extend Boas [B, Theorem 6.7].