- Tytuł:
- Fejér means of two-dimensional Fourier transforms on $H_p(ℝ × ℝ)$
- Autorzy:
- Weisz, Ferenc
- Powiązania:
- https://bibliotekanauki.pl/articles/1396031.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
p-atom
Hardy spaces
atomic decomposition
interpolation
Fejér means - Opis:
- The two-dimensional classical Hardy spaces $H_p(ℝ × ℝ)$ are introduced and it is shown that the maximal operator of the Fejér means of a tempered distribution is bounded from $H_p(ℝ × ℝ)$ to $L_p(ℝ^2)$ (1/2 < p ≤ ∞) and is of weak type $(H^{#}_1 (ℝ × ℝ), L_1(ℝ^2))$ where the Hardy space $H^#_1(ℝ × ℝ)$ is defined by the hybrid maximal function. As a consequence we deduce that the Fejér means of a function f ∈ $H_1^#(ℝ × ℝ)$ ⊃ $LlogL(ℝ^2)$ converge to f a.e. Moreover, we prove that the Fejér means are uniformly bounded on $H_p(ℝ × ℝ)$ whenever 1/2 < p < ∞. Thus, in case f ∈ $H_p(ℝ × ℝ)$, the Fejér means converge to f in $H_p(ℝ × ℝ)$ norm (1/2 < p < ∞). The same results are proved for the conjugate Fejér means.
- Źródło:
-
Colloquium Mathematicum; 1999, 82, 2; 155-166
0010-1354 - Pojawia się w:
- Colloquium Mathematicum
- Dostawca treści:
- Biblioteka Nauki
Artykuł