- Tytuł:
- Weighted inequalities for one-sided maximal functions in Orlicz spaces
- Autorzy:
- Ortega Salvador, Pedro
- Powiązania:
- https://bibliotekanauki.pl/articles/1217888.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
one-sided maximal functions
weighted inequalities
weights
Orlicz spaces - Opis:
- Let $M_{g}^{+}$ be the maximal operator defined by $M_{g}^{+}⨍(x) = \underset{h>0}{\text{sup}} (ʃ_{x}^{x+h} |⨍|g)/(ʃ_{x}^{x+h} g)$, where g is a positive locally integrable function on ℝ. Let Φ be an N-function such that both Φ and its complementary N-function satisfy $Δ_2$. We characterize the pairs of positive functions (u,ω) such that the weak type inequality $u({x ∈ ℝ | M_{g}^{+}⨍(x) > λ}) ≤ C/(Φ(λ)) \int_ℝ Φ(|⨍|)ω$ holds for every ⨍ in the Orlicz space $L_Φ(ω)$. We also characterize the positive functions ω such that the integral inequality $\int_ℝ Φ(|M_{g}^{+}⨍|)ω ≤ \int_ℝ Φ(|⨍|)ω$ holds for every $⨍ ∈ L_Φ(ω)$. Our results include some already obtained for functions in $L^p$ and yield as consequences one-dimensional theorems due to Gallardo and Kerman-Torchinsky.
- Źródło:
-
Studia Mathematica; 1998, 131, 2; 101-114
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł