- Tytuł:
- Some weighted inequalities for general one-sided maximal operators
- Autorzy:
-
J. Martín-Reyes, F.
de la Torre, A. - Powiązania:
- https://bibliotekanauki.pl/articles/1220679.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
one-sided maximal operators
Cesàro averages
weights - Opis:
- We characterize the pairs of weights on ℝ for which the operators $M_{h,k}^{+}f(x) = \underset{\text{sup}}{c>x}h(x,c) \int_{x}^{c} f(s)k(x,s,c)ds$ are of weak type (p,q), or of restricted weak type (p,q), 1 ≤ p < q < ∞, between the Lebesgue spaces with the coresponding weights. The functions h and k are positive, h is defined on ${(x,c): x < c}$, while k is defined on ${(x,s,c): x < s < c}$. If $h(x,c) = (c-x)^{-β}$, $k(x,s,c) = (c-s)^{α-1}$, 0 ≤ β ≤ α ≤ 1, we obtain the operator $M_{α,β}^{+}f = \underset{c>x}{\text{sup}} 1/(c-x)^{β} \int_{x}^{c} f(s)/(c-s)^{1-α} ds$. For this operator, under the assumption 1/p - 1/q = α - β, we extend the weak type characterization to the case p = q and prove that in the case of equal weights and 1 < p < ∞, weak and strong type are equivalent. If we take α = β we characterize the strong type weights for the operator $M_{α,α}^{+}$ introduced by W. Jurkat and J. Troutman in the study of $C_α$ differentiation of the integral.
- Źródło:
-
Studia Mathematica; 1997, 122, 1; 1-14
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł