Two-parameter maximal functions associated with degenerate homogeneous surfaces in ℝ³

• Autorzy: Gianfranco Marletta , Fulvio Ricci , Jacek Zienkiewicz
• Języki publikacji: EN

Abstrakty

EN

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 $p > max{3/2, 2k/(k+1)}$.

Kategorie tematyczne

• 32B25: Triangulation and related questions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 130
• Numer: 1
• Strony: 67-75

Daty

wydano

1998

otrzymano

1996-12-09

poprawiono

1998-01-12

Twórcy

autor

Gianfranco Marletta

• Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

autor

Fulvio Ricci

• Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

autor

Jacek Zienkiewicz

• Department of Mathematics, Wrocław University, Plac Grunwaldzki 2, 50-384 Wrocław, Poland

Bibliografia

• [MR] G. Marletta and F. Ricci, Two-parameter maximal functions associated with homogeneous surfaces in $ℝ^n$, this issue, 53-65.