Uniform convergence of double trigonometric series

Chen, Chang-Pao; Chen, Gwo-Bin

Studia Mathematica, Tome 119 (1996), p. 245-259 / Harvested from The Polish Digital Mathematics Library

Résumé

It is shown that under certain conditions on $c_{j k}$ , the rectangular partial sums $s_{m n} (x, y)$ converge uniformly on $T^{2}$ . These conditions include conditions of bounded variation of order (1,0), (0,1), and (1,1) with the weights |j|, |k|, |jk|, respectively. The convergence rate is also established. Corresponding to the mentioned conditions, an analogous condition for single trigonometric series is $\sum_{| k | = n}^{\infty} | Δ c_{k} | = o (1 / n)$ (as n → ∞). For O-regularly varying quasimonotone sequences, we prove that it is equivalent to the condition: $n c_{n} = o (1)$ as n → ∞. As a consequence, our result generalizes those of Chaundy-Jolliffe [CJ], Jolliffe [J], Nurcombe [N], and Xie-Zhou [XZ].

Publié le : 1996-01-01

Zbl 0849.42008

EUDML-ID : urn:eudml:doc:216276

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     title = {Uniform convergence of double trigonometric series},
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     volume = {119},
     year = {1996},
     pages = {245-259},
     zbl = {0849.42008},
     language = {en},
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Chen, Chang-Pao; Chen, Gwo-Bin. Uniform convergence of double trigonometric series. Studia Mathematica, Tome 119 (1996) pp. 245-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv118i3p245bwm/

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