Displaying similar documents to “Limit theorems for uniformly distributed p-adic sequences”

Weighted integrability and L¹-convergence of multiple trigonometric series

Chang-Pao Chen (1994)

Studia Mathematica

Similarity:

We prove that if c j k → 0 as max(|j|,|k|) → ∞, and ∑ | j | = 0 ± ∞ ∑ | k | = 0 ± ∞ θ ( | j | ⊤ ) ϑ ( | k | ⊤ ) | Δ 12 c j k | < ∞ , then f(x,y)ϕ(x)ψ(y) ∈ L¹(T²) and ∬ T ² | s m n ( x , y ) - f ( x , y ) | · | ϕ ( x ) ψ ( y ) | d x d y → 0 as min(m,n) → ∞, where f(x,y) is the limiting function of the rectangular partial sums s m n ( 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],...