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Weighted integrability of double cosine series with nonnegative coefficients

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Chen C.-P., Chen M.-C.

Studia Mathematica

2003

tom 156

nr 2

133-141

Let $f_{c}(x,y) ≡ ∑_{j=1}^{∞} ∑_{k=1}^{∞} a_{jk}(1 - cos jx)(1 - cos ky)$ with $a_{jk} ≥ 0$ for all j,k ≥ 1. We estimate the integral $∫_{0}^{π}∫_{0}^{π} x^{α-1} y^{β-1} ϕ(f_{c}(x,y)) dxdy$ in terms of the coefficients $a_{jk}$, 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].

Ograniczanie wyników

1 Studia Mathematica

1 Chen C.-P.

1 Chen M.-C.

1 2003

Wyniki wyszukiwania

Weighted integrability of double cosine series with nonnegative coefficients