- Tytuł:
- Weighted integrability and L¹-convergence of multiple trigonometric series
- Autorzy:
- Chen, Chang-Pao
- Tematy:
-
multiple trigonometric series
rectangular partial sums
Cesàro means
weighted integrability
L¹-convergence
conditions of generalized bounded variation - Pokaż więcej
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Powiązania:
- https://bibliotekanauki.pl/articles/1291177.pdf Link otwiera się w nowym oknie
- Opis:
- We prove that if $c_{jk} → 0$ as max(|j|,|k|) → ∞, and $∑_{|j|=0±}^∞ ∑_{|k|=0±}^∞ θ(|j|^⊤)ϑ(|k|^⊤)|Δ_{12}c_{jk}| < ∞$, then f(x,y)ϕ(x)ψ(y) ∈ L¹(T²) and $∬_{T²} |s_{mn}(x,y) - f(x,y)|·|ϕ(x)ψ(y)|dxdy → 0$ as min(m,n) → ∞, where f(x,y) is the limiting function of the rectangular partial sums $s_{mn}(x,y)$, (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].
- Dostawca treści:
- Biblioteka Nauki
Artykuł