Weighted integrability of double cosine series with nonnegative coefficients

Chang-Pao Chen; Ming-Chuan Chen

Studia Mathematica, Tome 157 (2003), p. 133-141 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $f_{c} (x, y) \equiv \sum_{j = 1}^{\infty} \sum_{k = 1}^{\infty} a_{j k} (1 - c o s j x) (1 - c o s k y)$ with $a_{j k} \geq 0$ for all j,k ≥ 1. We estimate the integral $\int_{0}^{π} \int_{0}^{π} x^{α - 1} y^{β - 1} ϕ (f_{c} (x, y)) d x d y$ in terms of the coefficients $a_{j k}$ , 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].

Publié le : 2003-01-01

Zbl 1021.42002

EUDML-ID : urn:eudml:doc:284752

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     title = {Weighted integrability of double cosine series with nonnegative coefficients},
     journal = {Studia Mathematica},
     volume = {157},
     year = {2003},
     pages = {133-141},
     zbl = {1021.42002},
     language = {en},
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Chang-Pao Chen; Ming-Chuan Chen. Weighted integrability of double cosine series with nonnegative coefficients. Studia Mathematica, Tome 157 (2003) pp. 133-141. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-2-4/