Two-parameter maximal functions associated with degenerate homogeneous surfaces in ℝ³
Studia Mathematica, Tome 130 (1998) no. 1, pp. 67-75
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We consider the two-parameter maximal operator $Mf(x)= sup_{a,b>0}$ ʃ_{|s| 1} |f(x-(as,bΓ(s)))|ds$ on a homogeneous surface $x_3 = Γ(x_1,x_2)$ in $ℝ^3$. We assume that the curvature of the level set $Γ(x_1,x_2) = 1$ has a degeneracy of finite order k at a given point. We prove that the operator M is bounded on $L^p$ if and only if $p > max{3/2, 2k/(k+1)}$.
@article{10_4064_sm_130_1_67_75,
author = {Gianfranco Marletta and Fulvio Ricci and Jacek Zienkiewicz},
title = {Two-parameter maximal functions associated with degenerate homogeneous surfaces in {\ensuremath{\mathbb{R}}{\textthreesuperior}}},
journal = {Studia Mathematica},
pages = {67--75},
year = {1998},
volume = {130},
number = {1},
doi = {10.4064/sm-130-1-67-75},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-130-1-67-75/}
}
TY - JOUR AU - Gianfranco Marletta AU - Fulvio Ricci AU - Jacek Zienkiewicz TI - Two-parameter maximal functions associated with degenerate homogeneous surfaces in ℝ³ JO - Studia Mathematica PY - 1998 SP - 67 EP - 75 VL - 130 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-130-1-67-75/ DO - 10.4064/sm-130-1-67-75 LA - en ID - 10_4064_sm_130_1_67_75 ER -
%0 Journal Article %A Gianfranco Marletta %A Fulvio Ricci %A Jacek Zienkiewicz %T Two-parameter maximal functions associated with degenerate homogeneous surfaces in ℝ³ %J Studia Mathematica %D 1998 %P 67-75 %V 130 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/sm-130-1-67-75/ %R 10.4064/sm-130-1-67-75 %G en %F 10_4064_sm_130_1_67_75
Gianfranco Marletta; Fulvio Ricci; Jacek Zienkiewicz. Two-parameter maximal functions associated with degenerate homogeneous surfaces in ℝ³. Studia Mathematica, Tome 130 (1998) no. 1, pp. 67-75. doi: 10.4064/sm-130-1-67-75
Cité par Sources :