- Tytuł:
- Two-parameter maximal functions associated with homogeneous surfaces in $ℝ^n$
- Autorzy:
-
Marletta, Gianfranco
Ricci, Fulvio - Powiązania:
- https://bibliotekanauki.pl/articles/1218365.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- Given a hypersurface $x_n = Ꮁ(x_1...,x_{n-1})$ in $ℝ^n$, where Ꮁ is homogeneous of degree d>0, we define the two-parameter maximal operator $ Mf(x) = sup_{a,b>0} ∫_{s∈ℝ^{n-1},|s| < 1} $ |f(x - (as, bᎱ(s)))|ds$. We prove that if d ≠ 1 and the hypersurface has non-vanishing Gaussian curvature away from the origin, then M is bounded on $L^p$ if and only if p>n/(n-1). If d = 1, i.e. if the surface is a cone, the same conclusion holds in dimension n ≥ 3 if the surface has n-1 non-vanishing principal curvatures away from the origin and it intersects the hyperplane $x_n = 0$ only at the origin.
- Źródło:
-
Studia Mathematica; 1998, 130, 1; 53-65
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł