- Tytuł:
- Cesàro summability of one- and two-dimensional trigonometric-Fourier series
- Autorzy:
- Weisz, Ferenc
- Powiązania:
- https://bibliotekanauki.pl/articles/966758.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
p-atom
Hardy spaces
Cesàro summability
atomic decomposition
p-quasilocal operator
interpolation - Opis:
- We introduce p-quasilocal operators and prove that if a sublinear operator T is p-quasilocal and bounded from $L_∞$ to $L_∞$ then it is also bounded from the classical Hardy space $H_p(T)$ to $L_p$ (0 < p ≤ 1). As an application it is shown that the maximal operator of the one-parameter Cesàro means of a distribution is bounded from $H_p(T)$ to $L_p$ (3/4 < p ≤ ∞) and is of weak type $(L_1,L_1)$. We define the two-dimensional dyadic hybrid Hardy space $H_{1}^{♯}(T^2)$ and verify that the maximal operator of the Cesàro means of a two-dimensional function is of weak type $(H_{1}^{♯}(T^2),L_1)$. So we deduce that the two-parameter Cesàro means of a function $f ∈ H_1^{♯}(T^2) ⊃ Llog L$ converge a.e. to the function in question.
- Źródło:
-
Colloquium Mathematicum; 1997, 74, 1; 123-133
0010-1354 - Pojawia się w:
- Colloquium Mathematicum
- Dostawca treści:
- Biblioteka Nauki
Artykuł