Restriction theorems for the Fourier transform to homogeneous polynomial surfaces in ℝ³

• Autorzy: E. Ferreyra , T. Godoy , M. Urciuolo
• Języki publikacji: EN

Abstrakty

EN

Let φ:ℝ² → ℝ be a homogeneous polynomial function of degree m ≥ 2, let Σ = {(x,φ(x)): |x| ≤ 1} and let σ be the Borel measure on Σ defined by $σ(A) = ∫_{B} χ_{A}(x,φ(x))dx$ where B is the unit open ball in ℝ² and dx denotes the Lebesgue measure on ℝ². We show that the composition of the Fourier transform in ℝ³ followed by restriction to Σ defines a bounded operator from $L^{p}(ℝ³)$ to $L^{q}(Σ,dσ)$ for certain p,q. For m ≥ 6 the results are sharp except for some border points.

Kategorie tematyczne

• 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 26D10: Inequalities involving derivatives and differential and integral operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 160
• Numer: 3
• Strony: 249-265

Daty

wydano

2004

Twórcy

autor

E. Ferreyra

• FaMAF, Universidad Nacional de Córdoba, and CIEM-CONICET, Ciudad Universitaria, 5000 Córdoba, Argentina

autor

T. Godoy

• FaMAF, Universidad Nacional de Córdoba, and CIEM-CONICET, Ciudad Universitaria, 5000 Córdoba, Argentina

autor

M. Urciuolo

• FaMAF, Universidad Nacional de Córdoba, and CIEM-CONICET, Ciudad Universitaria, 5000 Córdoba, Argentina

Identyfikatory

DOI

10.4064/sm160-3-4