Uniform convergence of double trigonometric series
Studia Mathematica, Tome 118 (1996) no. 3, pp. 245-259
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
It is shown that under certain conditions on ${c_{jk}}$, the rectangular partial sums $s_{mn}(x,y)$ 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 $∑_{|k|= n}^∞ |Δc_k| = o(1/n)$ (as n → ∞). For O-regularly varying quasimonotone sequences, we prove that it is equivalent to the condition: $nc_{n} = o(1)$ as n → ∞. As a consequence, our result generalizes those of Chaundy-Jolliffe [CJ], Jolliffe [J], Nurcombe [N], and Xie-Zhou [XZ].
@article{10_4064_sm_118_3_245_259,
author = {Chang-Pao Chen},
title = {Uniform convergence of double trigonometric series},
journal = {Studia Mathematica},
pages = {245--259},
year = {1996},
volume = {118},
number = {3},
doi = {10.4064/sm-118-3-245-259},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-118-3-245-259/}
}
Chang-Pao Chen. Uniform convergence of double trigonometric series. Studia Mathematica, Tome 118 (1996) no. 3, pp. 245-259. doi: 10.4064/sm-118-3-245-259
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