Geodesic
Two-parameter maximal functions associated with degenerate homogeneous surfaces in ℝ³
Studia Mathematica, Tome 130 (1998) no. 1, pp. 67-75

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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 $p > max{3/2, 2k/(k+1)}$.
DOI : 10.4064/sm-130-1-67-75

Gianfranco Marletta 1 ; Fulvio Ricci 1 ; Jacek Zienkiewicz 1

1 
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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

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