- Tytuł:
- On the uniform convergence and L¹-convergence of double Walsh-Fourier series
- Autorzy:
- Móricz, Ferenc
- Powiązania:
- https://bibliotekanauki.pl/articles/1293178.pdf
- Data publikacji:
- 1992
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Walsh-Paley system
W-continuity
moduli of continuity and smoothness
bounded variation in the sense of Hardy and Krause
generalized bounded variation
complementary functions in the sense of W. H. Young
rectangular partial sum
Dirichlet kernel
convergence in $L^p$-norm
uniform convergence Salem's test
Dini-Lipschitz test
Dirichlet-Jordan test - Opis:
- In 1970 C. W. Onneweer formulated a sufficient condition for a periodic W-continuous function to have a Walsh-Fourier series which converges uniformly to the function. In this paper we extend his results from single to double Walsh-Fourier series in a more general setting. We study the convergence of rectangular partial sums in $L^p$-norm for some 1 ≤ p ≤ ∞ over the unit square [0,1) × [0,1). In case p = ∞, by $L^p$ we mean $C_W$, the collection of uniformly W-continuous functions f(x, y), endowed with the supremum norm. As special cases, we obtain the extensions of the Dini-Lipschitz test and the Dirichlet-Jordan test for double Walsh-Fourier series.
- Źródło:
-
Studia Mathematica; 1992, 102, 3; 225-237
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł