Weighted integrability and L¹-convergence of multiple trigonometric series
Chen, Chang-Pao
Studia Mathematica, Tome 108 (1994), p. 177-190 / Harvested from The Polish Digital Mathematics Library
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We prove that if cjk→0 as max(|j|,|k|) → ∞, and ∑|j|=0±∞∑|k|=0±∞θ(|j|⊤)ϑ(|k|⊤)|Δ12cjk|<∞, then f(x,y)ϕ(x)ψ(y) ∈ L¹(T²) and ∬T²|smn(x,y)-f(x,y)|·|ϕ(x)ψ(y)|dxdy→0 as min(m,n) → ∞, where f(x,y) is the limiting function of the rectangular partial sums smn(x,y), (ϕ,θ) and (ψ,ϑ) are pairs of type I. A generalization of this result concerning L¹-convergence is also established. Extensions of these results to double series of orthogonal functions are also considered. These results can be extended to n-dimensional case. The aforementioned results generalize work of Balashov [1], Boas [2], Chen [3,4,5], Marzuq [9], Móricz [11], Móricz-Schipp-Wade [14], and Young [16].

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:216048 
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     author = {Chang-Pao Chen},
     title = {Weighted integrability and L$^1$-convergence of multiple trigonometric series},
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     year = {1994},
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     zbl = {0821.42007},
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Chen, Chang-Pao. Weighted integrability and L¹-convergence of multiple trigonometric series. Studia Mathematica, Tome 108 (1994) pp. 177-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv108i2p177bwm/

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